PHYSICS  DEPT. 


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LIBRARY 

OF     THE 

DEPARTMENT   OF   PHYSICS 


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SOME   CONTRIBUTIONS 


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LABORATORY   OF   PHYSICS 


OF  THE 

UNIVERSITY  OF  ILLINOIS 

o 

URBANA,  ILLINOIS 


for  1914-1919 
In  Two  Parts 

PART  I 


PHYSICS  oirr. 

SOME  CONTRIBUTIONS  FROM  THE  LABORATORY  OF 
PHYSICS,  UNIVERSITY  OF  ILLINOIS 

for  1914-1919 
Parti 


TABLE  OF  CONTENTS 

Acoustics  of  Auditoriums. — Bulletin  of  the  Engineering  Experiment  Sta- 
tion, University  of  Illinois,  March,  1914. 

F.   R.  Watson  ' 

A  Modified  Method  of  Measuring  e/m  and  v  for  Cathode  Rays. — Re- 
printed from  the  Physical  Review,  May,  1914. 

L.  T. Jones 

The  Determination  of  e/m  for  Cathode  Rays  as  a  Laboratory  Experiment 
for  an  Undergraduate  Course  in  Electrical  Measurements. — Re- 
printed from  School  Science  and  Mathematics,  October,  1914. 

C.  T.  Knipp 

An  Attempt  at  an  Electromagnetic  Emission  Theory  of  Light. — Reprinted 
from  the  Physical  Review,  June,  1914. 

J.  Kunz 

Some  Brush  Discharge  Phenomena  Produced  by  Continuous  Potentials. — 
Reprinted  from  the  Physical  Review,  July,  1914. 

S.  P.  Farwell 

The  Diffusion  of  Gases  at  Low  Pressures  Made  Visible  by  Color  Effects. — 
Reprinted  from  Science,  July  16,  1915. 

C.  T.  Knipp 

On  the  Present  Theory  of  Magnetism. — Reprinted  from  the  Physical  Re- 
view, August,  1915. 

J.  Kunz 

The  Absorption  of  Air  by  Charcoal  Cooled  to  the  Temperature  of  Liquid 
Air. — Reprinted  from  Science,  September,  1915. 

f~*      T1      T7" 

L.  1 .  Knipp 

Acoustics  of  Auditoriums. — Reprinted  from  The  Brickbuilder,  October, 
1915. 

F.  R.  Watson 

Saturation  Value  of  the  Intensity  of  Magnetization  and  the  Theory  of 
the  Hysteresis  Loop. — Reprinted  from  the  Phys'cal  Review,  Novem- 
ber, 1915. 

E.  H.  Williams 


Color  Effects  of  Positive  and  of  Cathode  Rays  in  Residual  Air,  Hydrogen, 
Helium,  etc. — Reprinted  from  Science,  December  31,  1915. 

C.  T.  Knipp 

The  Structure  of  T  Rays  on  the  Basis  of  the  Electro-Magnetic  Theory  of 
Light. — Reprinted  from  the  Physical  Review,  December,  1915. 

J.  Kunz 

On  the  Construction  of  Sensitive  Photoelectric  Cells. — Reprinted  from 
the  Physical  Review,  January,  1916. 

J.  Kunz  and  J.  Stebbins 

An  Investigation  of  the  Transmission,  Reflection  and  Absorption  of  Sound 
by  Different  Materials. — Reprinted  from  the  Physical  Review,  Jan- 
uary, 1916. 

F.  R.  Watson  3 

A  Study  of  Ripple  Wave  Motion. — Reprinted  from  the  Physical  Review, 
February,  1916. 

F.  R.  Watson  and  W.  A.  Shewhart 

Photographs  Showing  the  Relative  Deflection  of  the  Positive  and  of  the 
Negative  Ions  as  Compared  with  that  of  the  Electron. — Reprinted 
from  Science,  March  17,  1916. 

C.  T.  Knipp 

Electrical  Discharge  Between  Concentric  Cylindrical  Electrodes. — Re- 
printed from  Science,  June  2,  1916. 

C.  T.  Knipp 

Retrograde  Rays  from  the  Cold  Cathode. — Reprinted  from  the  Physical 
Review,  June,  1916. 

O.  H.  Smith 

An  Experimental  Verification  of  the  Law  of  Variation  of  Mass  with  Ve- 
locity for  Cathode  Rays. — Reprinted  from  the  Physical  Review, 
July,  1916. 

L.  T.  Jones 

On  the  Initial  Condition  of  the  Corona  Discharge. — Reprinted  from  the 
Physical  Review,  July,  1916. 

J.  Kunz 

Determination  of  the  Laws  Relating  lonization  Pressure  to  the  Current 
in  the  Corona  of  Constant  Potentials. — Reprinted  from  the  Physical 
Review,  September,  1916. 

E.  H.  Warner 

Direct  Current  Corona  from  Different  Surfaces  and  Metals. — Reprinted 
from  the  Physical  Review,  October,  1916. 

S.  J.  Crooker 


To  Cut  Off  Large  Tubes  of  Pyrex  Glass. — Reprinted  from  Science,  May  9, 
1919.  C.  T.  Knipp 

Tolman's  Transformation  Equations,  the  Photoelectric  Effect  and  Radi- 
ation Pressure. — Reprinted  from  the  Physical  Review,  March,  1917. 

S.  Karrer 

An  Improved  High  Vacuum  Mercury  Vapor  Pump. — Reprinted  from  the 
Physical  Review,  March,  1917. 

C.  T.  Knipp 

A  Simple  Demonstration  Tube  for  Exhibiting  the  Mercury  Hammer,  Glow 
by  Mercury  Friction,  and  the  Vaporization  of  Mercury  at  Reduced 
Pressure. — Reprinted  from  School  Science  and  Mathematics,  May, 
1917. 

C.  T.  Knipp 

Distribution  of  Potential  in  a  Corona  Tube. — Reprinted  from  the  Physical 
Review,  September,  1917. 

H.  T.  Booth 

The  Pressure  Increase  in  the  Corona. — Reprinted  from  the  Physical  Re- 
view, November,  1917. 

E.  H.  Warner 

On  Bohr's  Atom  and  Magnetism.— Reprinted  from  the  Physical  Review, 
July,  1918. 

J.  Kunz 

The  Magnetic  Properties  of  Some  Rare  Earth  Oxides  as  a  Function  of  the 
Temperature. — Reprinted  from  the  Physical  Review,  August,  1918. 

E.H.Williams 

Amplification  of  the  Photoelectric  Current  by  Means  of  the  Audion. — Re- 
printed from  the  Physical  Review,  February,  1919. 

C.  E.  Pike 


UNIVERSITY  OF  ILLINOIS 
ENGINEERING  EXPERIMENT  STATION 

BULLETIN  No.  73  MARCH,  1914 

ACOUSTICS  OF  AUDITORIUMS. 
BY  F.  R.  WATSON,  ASSISTANT  PROFESSOR  OF  PHYSICS. 

CONTENTS.  page 

I.     Introduction 3 

Acknowledgment    5 

II.     Behavior  of  Sound  Waves  in  a  Room 5 

III.  Methods  of  Improving  Faulty  Acoustics 8 

A.  Reverberation  and  Its  Cure 8 

Experimental  Work  on  Cure  of  Reverberation 9 

Formulae  for  Reverberation  of  Sound  in  a  Room 10 

B.  Echoes  and  Their  Remedy 11 

C.  Popular  Conception  of  Cures.    Use  of  Wires  and  Sound- 

ing Boards  • 11 

Sounding  Boards  12 

Modeling  New  Auditorium  after  Old  Ones  with  Good 

Acoustics    12 

D.  The  Effect  of  the  Ventilation  System  on  the  Acoustics. ..  13 

IV.  The  Investigation  in  the  Auditorium  at  the  University  of 

Illinois    13 

A.  Preliminary  Work 13 

B.  Details  of  the  Acoustical  Survey  in  the  Auditorium 17 

C.  Conclusion  Drawn  from  the  Acoustical  Survey 26 

D.  Methods  Employed  to  Improve  the  Acoustics 26 

Reflecting  Boards    26 

Sabine's  Method    26 

Method  of  Eliminating  Echoes 29 

Proposed  Final  Cure. , 29 

V.     Bibliography  of  Publications  on  Acoustics  of  Auditoriums. . .  31 


ACOUSTICS  OF  AUDITORIUMS 

AN  INVESTIGATION  OF  THE  ACOUSTICAL  PROPERTIES  OF  THE  AUDITORIUM 
AT  THE  UNIVERSITY  OF  ILLINOIS. 

I.     INTRODUCTION. 

Much  concern  has  arisen  <in  late  years  in  the  minds  of  architects 
because  of  the  faulty  acoustics  that  exist  in  many  auditoriums.  The 
prevalence  of  echoes  and  reverberations  with  the  consequent  difficulty 
in  hearing  and  understanding  on  the  part  of  the  auditor  defeats  the 
purpose  of  the  auditorium  and  diminishes  its  value. 

The  Auditorium  at  the  University  of  Illinois  presents  such  a  case. 
The  building  is  shaped  nearly  like  a  hemisphere,  with  several  large 
arches  and  recesses  to  break  up  the  regularity  of  its  inner  surface.  The 
original  plans  of  the  architect  were  curtailed  because  of  insufficient 
money  appropriated  for  the  construction.  The  interior  of  the  hall,  there- 
fore, was  built  absolutely  plain  with  almost  no  breaking  up  of  the  large, 
smooth  wall  surfaces;  and,  at  first,  there  were  no  furnishings  except  the 
seats  and  the  cocoa  matting  in  the  aisles.  The  acoustical  properties 
proved  to  be  very  unsatisfactory.  A  reverberation  or  undue  prolonga- 
tion of  the  sound  existed,  and  in  addition,  because  of  the  large  size  of 
the  room  and  the  form  and  position  of  the  walls,  echoes  were  set  up. 

If  an  observer  stood  on  the  platform  and  clapped  his  hands,  a 
veritable  chaos  of  sound  resulted.  Echoes  were  heard  from  every  direc- 
tion and  reverberations  continued  for  a  number  of  seconds  before  all 
was  still  again.  Speakers  found  their  utterances  thrown  back  at  them, 
and  auditors  all  over  the  house  experienced  difficulty  in  understanding 
what  was  said.  On  one  occasion  the  University  band  played  a  piece 
which  featured  a  xylophone  solo  with  accompaniment  by  the  other  instru- 
ments. It  so  happened  that  the  leader  heard  the  echo  more  strongly 
than  the  direct  sound  and  beat  time  with  it.  Players  near  the  xylophone 
kept  time  to  the  direct  sound,  while  those  farther  away  followed  the 
echo.  The  confusion  may  well  be  imagined. 

Thus  it  seemed  that  the  Auditorium  was  doomed  to  be  an  acoustical 
horror ;  that  speakers  and  singers  would  avoid  it,  and  that  auditors  would 
attend  entertainments  in  it  only  under  protest.  But  the  apparent  mis- 
fortune was  in  one  way  a  benefit  since  it  provided  an  opportunity  to 


4 


ILLINOIS    ENGINEERING    EXPERIMENT    STATION 


FIG.  2.     PHOTOGRAPH  OF  INTERIOR.    VIEW  OF  STAGE. 


ji^llRIIHH^. 

/^l  BK 


FIG.  3.    PHOTOGRAPH  OF  INTERIOR.    VIEW  TOWARD  BALCONY 


WATSON — ACOUSTICS    OF    AUDITORIUMS  5 

study  defective  acoustics  under  exceptionally  good  conditions  and  led 
to  conclusions  that  not  only  allowed  the  Auditorium  to  be  improved  but 
also  indicate  some  of  the  pitfalls  to  be  avoided  in  future  construction  of 
other  halls. 

An  investigation  of  the  acoustical  properties  of  the  Auditorium  was" 
begun  in  1908  and  has  continued  for  six  years.  It  was  decided  at  the 
outset  not  to  use  "cut  and  try"  methods  of  cure,  but  to  attack  the  prob- 
lem systematically  so  that  general  principles  could  be  found,  if  possible, 
that  would  apply  not  only  to  the  case  being  investigated  but  to  audi- 
toriums in  general.  This  plan  of  procedure  delayed  the  solution  of  the 
problem,  since  it  became  necessary  to  study  the  theory  of  sound  and 
carry  out  laboratory  investigations  at  the  same  time  that  the  complex 
conditions  in  the  Auditorium  were  being  considered.  The  author  spent 
one  year  of  the  six  abroad  studying  the  theory  of  acoustics  and  inspect- 
ing various  auditoriums. 

The  main  echoes  in  the  Auditorium  were  located  by  means  of  a  new 
method  for  tracing  the  path  of  sound,  the  time  of  reverberation  was 
determined  by  Sabine's  method,  and  a  general  diagnosis  of  the  acoustical 
defects  was  made.  Hangings  and  curtains  were  installed  in  accordance 
with  the  results  of  the  study  so  that  finally  the  acoustical  properties  were 
improved. 

Acknowledgment. — The  author  desires  to  express  his  great  appre- 
ciation of  the  advice  and  encouragement  given  by  President  E.  J.  James, 
Supervising  Architect  J.  M.  White,  and  Professor  A.  P.  Carman  of  the 
Physics  Department.  He  desires  also  to  acknowledge  the  material  assist- 
ance cheerfully  rendered  by  the  workmen  at  the  University,  which  con- 
tributed in  no  small  degree  to  the  successful  solution  of  the  problem. 

II.     BEHAVIOR  OF  SOUND  WAVES  IN  A  ROOM. 

When  a  speaker  addresses  an  audience,  the  sounds  he  utters  proceed 
in  ever  widening  spherical  waves  until  they  strike  the  boundaries  of  the 
room.  Here  the  sound  is  partly  reflected,  partly  transmitted,  and  the 
rest  absorbed.  The  amounts  of  reflection,  absorption  and  transmission 
depend  on  the  character  of  the  walls.  A  hard,  smooth  wall  reflects  most 
of  the  sound  so  that  but  little  is  transmitted  or  absorbed.  In  the  case 
of  a  porous  wall  or  a  yielding  wall,  the  absorption  and  transmission 
are  greater,  and  the  reflection  is  less.  After  striking  a  number  of  re- 
flecting surfaces,  the  energy  is  used  up  and  the  sound  dies  out. 


6  ILLINOIS    ENGINEERING    EXPERIMENT    STATION 

The  reflection  of  sound  produces  certain  advantages  and  disadvan- 
tages for  the  acoustics.  When  it  is  considered  that  sound  travels  about 
1100  feet  a  second  it  may  be  seen  that  a  room  of  ordinary  size  is  almost 
immediately  filled  with  sound  because  of  the  many  reflections.  In  a 
room  40  feet  square,  for  instance,  the  number  of  reflections  per  second 
between  opposite  walls  is  1100  -f-  40,  or  approximately  27.  The  num- 
ber is  really  greater  than  this,  since  the  sound  that  goes  into  the  corners 
is  reflected  much  more  frequently  than  out  in  the  middle  where  the 
distances  between  walls  are  greater.  The  result  is  that  the  sound  mixes 
thoroughly  in  all  parts  of  the  room  so  as  to  give  the  same  average  in- 
tensity ;  that  is,  the  sound  is  of  the  same  average  loudness  for  all  auditors, 
even  for  those  in  the  remotest  corners. 

Though  the  reflection  of  sound  has  the  advantage  of  fulfilling  the 
conditions  for  loudness,  it  introduces  at  the  same  time  possibilities  for 
setting  up  defective  acoustics.  For  instance,  when  the  walls  of  the  room 
are  hard  and  smooth  very  little  energy  is  lost  at  each  impact  of  the 
sound  and  many  reflections  take  place  before  it  finally  dies  out.  This 
slow  decadence  of  the  sound,  or  reverberation  as  it  is  called,  is  the  most 
common  defect  in  auditoriums. 

If  a  speaker  talks  in  such  a  hall  the  auditors  have  difficulty  in 
understanding.  Each  sound,  instead  of  dying  out  quickly,  persists  for 
some  time  so  that  the  succeeding  words  blend  with  their  predecessors 
and  set  up  a  mixture  of  sounds  which  produces  confusion.  The  cure  for 
the  trouble  is  brought  about  by  the  introduction  of  materials  such  as 
carpets,  tapestries,  and  the  like,  which  act  as  absorbers  of  sound  and 
reduce  the  time  of  reverberation. 

When  music  is  played  in  an  auditorium  with  a  prolonged  reverbera- 
tion, the  tones  following  one  another  blend  and  produce  the  same  effect 
as  that  of  a  piano  when  played  with  the  loud  pedal  in  use.  A  reverbera- 
tion is  more  advantageous  for  music  than  for  speech,  since  the  pro- 
longation and  blending  of  the  musical  tones  is  desired,  but  the  mixing 
of  the  words  in  a  speech  is  a  distinct  disadvantage.  When  curing  this 
defect  for  halls  used  for  both  music  and  speaking,  a  middle  course  must 
be  steered,  so  that  the  reverberation  is  made  somewhat  long  for  speaking 
and  somewhat  short  for  music,  yet  fairly  satisfactory  for  both. 

Going  back  to  the  consideration  of  the  reflection  of  sound,  it  is 
found  that  another  defect  may  be  produced,  namely,  an  echo.  This  is  the 
case  when  a  wall  at  some. distance  reflects  the  sound  to  the  position  of  the 
auditor.  He  hears  the  sound  first  from  the  speaker,  then  later  by  reflec- 


WATSON ACOUSTICS    OF    AUDITORIUMS  7 

tion  from  the  wall.  The  time  interval  between  the  direct  and  reflected 
sound  must  be  great  enough  to  allow  two  distinct  impressions  to  be 
made.  This  time  is  about  1/15  of  a  second,  but  varies  with  the  acute- 
ness  of  the  observer.  The  farther  off  the  wall  is,,  the  greater  is  the  time 
interval  and  the  more  pronounced  is  the  echo.  If  the  wall  is  not  very 
distant,  the  time  interval  is  too  short  to  allow  two  distinct  impressions 
to  be  made,  and  the  effect  on  the  auditor  is  then  much  the  same  as  if 
his  neighbor  at  his  side  speaks  the  words  of  the  discourse  in  his  ear  at 
the  same  time  that  he  gets  them  directly  from  the  speaker.  In  case  the 
reflecting  wall  is  curved  so  as  to  focus  the  sound  the  echoes  are  much 
more  pronounced.  A  curved  wall  wherever  it  may  be  placed  in  an  audi- 
torium is  thus  always  a  menace  to  good  acoustics. 

There  are  other  actions  of  the  sound  that  may  result  in  acoustical 
defects.  The  phenomena  of  resonance,  for  instance,  may  cause  trouble. 
Suppose  that  the  waves  of  sound  impinge  on  an  elastic  wall,  not  too 
rigid.  If  these  waves  are  timed  right  they  set  the  wall  in  vibration  in 
the  same  way  that  the  bell  ringer  causes  a  bell  to  ring  by  a  succession 
of  properly  timed  pulls  on  the  bell  rope.  The  wall  of  the  room  will  then 
vibrate  under  the  action  of  the  sound  with  which  it  is  in  tune  and  will 
reinforce  it.  Now  suppose  a  band  is  playing  in  a  room.  Certain  tones 
are  reinforced,  while  the  others  are  not  affected.  The  original  sound  is 
then  distorted.  The  action  is  the  same  on  the  voice  of  the  speaker.  The 
sounds  he  utters  are  complex  and  as  they  reach  the  walls  certain  com- 
ponents are  reinforced  and  the  quality  of  the  sound  is  changed.  This 
action  of  resonance  may  also  be  caused  by  the  air  in  a  room.  Each 
room  has  a  definite  pitch  to  which  it  responds,  the  smaller  the  volume 
of  the  room  the  higher  being  the  pitch.  A  large  auditorium  would 
respond  to  the  very  low  pitch  of  the  bass  drum.  In  small  rooms  and 
alcoves  the  response  is  made  to  higher  pitched  tones,  as  may  be  observed 
by  singing  the  different  notes  of  the  scale  until  a  resonance  is  obtained. 

Another  action  of  sound  causes  the  interference  of  waves.  Thus 
the  reflected  waves  may  meet  the  oncoming  ones  and  set  up  concentra- 
tions of  sound  in  certain  positions  and  a  dearth  of  sound  in  others. 

Summing  up,  it  is  seen  that  the  effects  of  sound  which  may  exist 
in  a  room  are  loudness,  reverberation,  echoes,  resonance,  and  interference, 
and  that  the  most  common  defects  are  reverberation  and  echoes.  We 
now  turn  to  the  discussion  of  the  methods  of  cure. 


8  ILLINOIS    ENGINEERING    EXPERIMENT    STATION 

III.     METHODS  OF  IMPROVING  FAULTY  ACOUSTICS. 

A.       REVERBERATION  AND   ITS    CURE. 

Everyone  has  doubtless  observed  that  the  hollow  reverberations  in 
an  empt}^  house  disappear  when  the  house  is  furnished.  So,  in  an  audi- 
torium, the  reverberation  is  lessened  when  curtains,  tapestries,  and  the 
like  are  installed  in  sufficient  numbers.  The  reason  for  this  action  is 
found  when  we  inquire  what  ultimately  becomes  of  the  sound. 

Sound  is  a  form  of  energy  and  energy  can  not  be  destroyed.  When 
it  finally  dies  out,  the  sound  must  be  changed  to  some  other  form  of 
energy.  In  the  case  of  the  walls  of  a  room,  for  instance,  it  has  been 
shown  in  a  preceding  paragraph  that  the  sound  may  be  changed  into 
mechanical  energy  in  setting  these  walls  in  vibration.  Again,  some  of 
the  sound  may  pass  out  through  open  windows  and  thus  disappear.  The 
rest  of  the  sound,  according  to  Lord  Rayleigh,  is  transformed  by  friction 
into  heat.  Thus1  a  high  pitched  sound,  such  as  a  hiss,  before  it  travels 
any  great  distance  is  killed  out  by  the  friction  of  the  air.  Lower  pitched 
sounds,  on  reaching  a  wall,  set  up  a  friction  in  the  process  of  reflection 
between  the  air  particles  and  the  wall  so  that  some  of  the  energy  is  con- 
verted into  heat.2  The  amount  of  sound  energy  thus  lost  is  small  if  the 
walls  are  hard  and  smooth.  The  case  is  much  different,  however,  if  the 
walls  are  rough  and  porous,  since  it  appears  that  the  friction  in  the 
pores  dissipates  the  sound  energy  into  heat.  In  this  connection,  Lamb3 
writes :  "In  a  sufficiently  narrow  tube  the  waves  are  rapidly  stifled,  the 
mechanical  energy  lost  being  of  course  converted  into  heat.  *  *  *  * 
When  a  sound  wave  impinges  on  a  slab  which  is  permeated  by  a  large 
number  of  very  minute  channels,  part  of  the  energy  is  lost,  so  far  as 
the  sound  is  concerned,  by  dissipation  within  these  channels  in  the  way 
just  explained.  The  interstices  in  hangings  and  carpets  act  in  a  similar 
manner,  and  it  is  to  this  cause  that  the  effect  of  such  appliances  in 
deadening  echoes  in  a  room  is  to  be  ascribed,  a  certain  proportion  of  the 
energy  being  lost  at  each  reflection.  It  is  to  be  observed  that  it  is  only 
through  the  action  of  tru£  dissipative  forces,  such  as  viscosity  and  thermal 
conduction,  that  sound  can  die  out  in  an  enclosed  space,  no  mere  modi- 
fications of  the  waves  by  irregularities  being  of  any  avail." 

It  should  be  pointed  out  in  this  connection  that  any  mechanical 
breaking  up  of  the  sound  by  relief  work  on  the  walls  or  by  obstacles  in 
the  room  will  not  primarily  diminish  the  energy  of  the  sound.  These 

1.  "Theory  of   Sound,"  Vol.   II,   p.   316. 

2.  "Theory  of   Sound,"   Vol.   II,   §   351. 

3.  "Dynamical  Theory  of   Sound,"  p.    196. 


WATSON — ACOUSTICS    OF    AUDITORIUMS  0 

may  break  up  the  regular  reflection  and  eliminate  echoes,  but  the  sound 
energy  as  such  disappears  only  when  friction  is  set  up. 

The  following  quotation  from  Rayleigh1  emphasizes  these  conclu- 
sions: "In  large  spaces,  bounded  by  non-porous  walls,  roof,  and  floor, 
and  with  few  windows,  a  prolonged  resonance  seems  inevitable.  The 
mitigating  influence  of  thick  carpets  in  such  cases  is  well  known.  The 
application  of  similar  material  to  the  walls  and  roof  appears  to  offer  the 
best  chance  of  further  improvement/' 

Experimental  Work  on  Cure  of  Reverberation. — The  most  impor- 
tant experimental  work  in  applying  this  principle  of  the  absorbing  power 
of  carpets,  curtains,  etc.,  has  been  done  by  Professor  Wallace  C.  Sabine 
of  Harvard  University.2  In  a  set  of  interesting  experiments  lasting 
over  a  period  of  four  years,  he  was  able  to  deduce  a  general  relation 
between  t,  the  time  of  reverberation,  V,  the  volume  of  the  room,  and  a, 
the  absorbing  power  of  the  different  materials  present.  Thus: 

*  =  0.164  V^-a  (1) 

For  good  acoustical  conditions,  that  is,  for  a  short  time  of  reverbera- 
tion, the  volume  V  should  be  small  and  the  absorbing  materials,  repre- 
sented by  a,  large.  This  is  the  case  in  a  small  room  with  plenty  of 
curtains  and  rugs  and  furniture.  If,  however,  the  volume  of  the  room 
is  great,  as  in  the  case  of  an  auditorium,  and  the  amount  of  absorbing 
materials  small,  a  troublesome  reverberation  will  result. 

Professor  Sabine  determined  the  absorbing  powers  of  a  number  of 
different  materials.  Calling  an  open  window  a  perfect  absorber  of  sound, 
the  results  obtained  may  be  written  approximately  as  follows: 

One  square  meter  of  open  window  space 1.000 

One  square  meter  of  glass,  plaster,  or  brick 025 

One  square  meter  of  heavy  rugs,  curtains,  etc 25 

One  square  meter  of  hair  felt,  1  inch  thick 75 

One  square  meter  of  audience    . 96 

These  values,  together  with  the  formula,  allow  a  calculation  to  be 
made  in  advance  of  construction  for  the  time  of  reverberation.  This 
pioneer  work  cleared  the  subject  of  architectural  acoustics  from  the  fog 
of  mystery  that  hung  over  it  and  allowed  the  essential  principles  to  be 
seen  in  the  light  of  scientific  experiment. 

In  a  later  investigation3  Sabine  showed  that  the  reverberation  de- 
pended also  on  the  pitch  of  sound.  As  a  concrete  example,  the  high 

1.  "Theory  of  Sound,"  p.  333. 

2.  "Architectural  Acoustics."     A  series  of  articles  in  the  Engineering  Record,  1900;  also 
the   American   Architect,   1900. 

3.  "Architectural  Acoustics,"  Proc.   of  Amer.  Acad.   of  Arts  arid  Sciences.     Vol.  42,  pp. 
49-84,    1906. 


10  ILLINOIS    ENGINEERING    EXPERIMENT    STATION 

notes  of  a  violin  might  be  less  reverberant  with  a  large  audience  than 
the  lower  tones  of  the  bass  viol,  although  both  might  have  the  same 
reverberation  in  the  room  with  no  audience.  Again,  the  voice  of  a  man 
with  notes  of  low  pitch  might  give  satisfactory  results  in  an  auditorium 
while  the  voice  of  a  woman  with  higher  pitched  notes  would  be  unsat- 
isfactory. 

These  considerations  show  that  the  acoustics  in  an  auditorium  vary 
with  other  factors  than  the  volume  of  the  room^  and  the  amount  of 
absorbing  material  present.  The  audience  may  be  large  or  small,,  the 
speaker's  voice  high  or  low,  the  entertainment  a  musical  number  or  an 
address.  The  best  arrangement  for  good  acoustics  is  then  a  compromise 
where  the  average  conditions  are  satisfied.  The  solution  offered  by 
Professor  Sabine  is  such  an  average  one,  and  has  proved  satisfactory  in 
practice. 

The  problem  of  architectural  acoustics  has  been  attacked  experi- 
mentally by  other  workers.  Stewart1  proposed  a  cure  for  the  poor 
acoustical  conditions  in  the  Sibley  Auditorium  at  Cornell  University. 
His  experiments  confirmed  the  work  of  Sabine.  Marage2,  after  investi- 
gating the  properties  of  six  halls  in  Paris,  approved  Sabine's  results  and 
advocated  a  time  of  reverberation  of  from  ^  to  1  second  for  the  case  of 
speech. 

Formulae  for  Reverberation  of  Sound  in  a  Room. — On  the  theo- 
retical side,  Sabine's  formula  has  been  developed  by  Franklin3,  who  ob- 
tained the  relation  t  =  0.1625  V  -f-  a,  an  interesting  confirmation,  since 
Sabine's  experimental  value  for  the  constant  was  0.164. 

A  later  development  has  been  given  by  Jager,4  who  assumes  for  a 
room  whose'  dimensions  are  not  greater  than  about  60  feet,  that  the 
sound,  after  filling  the  room,  passes  equally  in  all  directions  through 
any  point,  and  that  the  average  energy  is  the  same  in  different  parts  of 
the  room.  By  using  the  theory  of  probability  and  considering  that  a 
beam  of  sound  in  any  direction  may  be  likened  to  a  particle  with  a 
definite  velocity,  he  was  able  to  deduce  Sabine's  formula  and  write  down 
the  factors  that  enter  into  the  constants.  Applying  his  results  to  the 
case  of  reflection  of  sound  from  a  wall,  he  showed  that  sound  would  be 
reflected  in  greater  volume  when  the  mass  of  the  wall  was  increased  and 


1.  G.    W.    Stewart.      "Architectural    Acoustics,"    Sibley    Journal    of    Engineering,    May, 
1903.     Published   by   Cornell   University,  Ithaca,   N.    Y. 

2.  "Qualites  acoustiques  de  certaines  salles  pour  la  voix  parlee."     Comptes  Rendus,  142, 
'878,  1906. 

3.  W.    S.   Franklin.     "Derivation  of  Equation  of  Decaying  Sound  in  a  Room  and  Defi- 
nition   of    Open    Window    Equivalent    of   Absorbing   Power."      Physical    Review,    Vol.    16,    pp. 
372-374,   1903. 

4.  G.    Jager.      "Zur    Theorie    des    Nachhslls."      Sitzungsberichte    der    Kaiserliche    Akad. 
der  Wissenschaften  in  Wien,  Math-naturw.  Klasse;   Bd.   CXX.  Abt.   11  a.   Mai,   1911. 


WATSON ACOUSTICS    OF    AUDITORIUMS  11 

the  pitch  of  the  sound  made  higher.  He  showed  also  that  when  sound 
impinges  on  a  porous  wall,  more  energy  is  absorbed  when  the  pitch  of 
the  sound  is  high  than  when  it  is  low,  since  the  vibrations  of  the  air 
are  more  frequent,  and  more  friction  is  introduced  in  the  interstices 
of  the  material. 

B.       ECHOES  AND  THEIR  REMEDY. 

An  echo  is  set  up  by  a  reflecting  wall.  If  an  observer  stands  some 
distance  from  the  front  of  a  cliff  and  claps  his  hands,  or  shouts,  he 
finds  that  the  sound  is  returned  to  him  from  the  cliff  as  an  echo.  So, 
in  an  auditorium,  an  auditor  near  the  speaker  gets  the  sound  first 
directly  from  the  speaker,  then,  an  instant  later,  a  strong  repetition  of 
the  sound  by  reflection  from  a  distant  wall.  This  echo  is  more  pro- 
nounced if  the  wall  is  curved  and  the  auditor  is  at  the  point  where  the 
sound  is  focused. 

To  cure  such  an  echo,  two  methods  may  be  considered.  One  method 
consists  in  changing  the  form  of  the  wall  so  that  the  reflected  sound  no 
longer  sets  up  the  echo.  That  is,  either  change  the  angle  of  the  wall, 
so  that  the  reflected  sound  is  sent  in  a  new  direction  where  it  may  be 
absorbed  or  where  it  may  reinforce  the  direct  sound  without  producing 
any  echoes,  or  else  modify  the  surface  of  the  wall  by  relief  work  or  by 
panels  of  absorbing  material,  so  that  the  strong  reflected  wave  is  broken 
up  and  the  sound  is  scattered.  The  second  method  is  to  make  the 
reflecting  wall  a  "perfect"  absorber,  so  that  the  incident  sound  is  swal- 
lowed up  and  little  or  none  reflected.  These  methods  have  been  desig- 
nated as  "surgical"  and  "medicinal"  respectively.  Each  method  has  its 
disadvantages.  Changing  the  form  of  the  walls  in  an  auditorium  is 
likely  to  do  violence  to  the  architectural  design.  On  the  other  hand, 
there  are  no  perfect  absorbers,  except  open  windows,  and  these  can  sel- 
dom be  applied.  The  cure  in  each  case  is,  then,  a  matter  of  study  of 
the  special  conditions  of  the  auditorium.  Usually  a  combination  of  the 
surgical  and  the  medicinal  cures  is  adopted.  For  instance,  coffering  a 
wall  so  that  panels  of  absorbing  material  may  be  introduced  has  been 
found  to  work  well  in  bettering  the  acoustics,  and  also,  in  many  cases, 
it  fits  in  with  the  architectural  features. 

C.       POPULAR     CONCEPTION     OF     CURES. USE    .OF     WIRES     AND     SOUNDING 

BOARDS. 

A  few  words  should  be  written  concerning  the  popular  notion  that 
wires  and  sounding  boards  are  effective  in  curing  faulty  acoustics.  Ex- 
periments and  observations  show  that  wires  are  of  practically  no  benefit, 


12  ILLINOIS    ENGINEERING   EXPERIMENT    STATION 

and  sounding  boards  can  be  used  only  in  special  cases.  Wires  stretched 
in  a  room  scarcely  affect  the  sound,  since  they  present  too  small  a  sur- 
face to  disturb  the  waves.  They  have  much  the  same  eifect  on  sound 
waves  that  a  fish  line  in  the  water  has  on  water  waves.  The  idea 
has,  perhaps,  grown  into  prominence  because  of  the  action  of  a  piano 
in  responding  to  the  notes  of  a  singer.  The  piano  has  every  advantage 
over  a  wire  in  an  auditorium.  It  has  a  large  number  of  strings  tuned 
to  different  pitches  so  that  it  responds  to  any  note  sung.  It  also  has  a 
sounding  board  that  reinforces  strongly  the  sound  of  the  strings. 
Finally,  the  singer  is  usually  near  the  piano.  The  wire  in  the  auditorium 
responds  to  only  one  tone  of  the  many  likely  to  be  present,  it  has  no 
sounding  board,  and  the  singer  is  some  distance  away.  But  little  effect, 
therefore,  is  to  be  expected. 

The  author  has  visited  a  number  of  halls  where  wires  have  been 
installed,  and  has  yet  to  find  a  case  where  pronounced  improvement  has 
resulted.1  Sabine2  cites  a  case  where  five  miles  of  wire  were  stretched 
in  a  hall  without  helping  the  acoustical  conditions.  It  is  curious  that 
so  erroneous  a  conception  has  grown  up  in  the  public  mind  with  so  little 
experimental  basis  to  support  it. 

Sounding  Boards. — Sounding  boards  or,  more  properly,  reflecting 
boards,  have  value  in  special  cases.  Some  experiments  are  described 
later  where  pronounced  effects  were  obtained.  The  sounding  board 
should  be  of  special  design  to  fit  the  conditions  under  which  it  is  to 
be  used. 

Modeling  New  Auditoriums  after  Old  Ones  with  Good  Acoustics. — 
Another  suggestion  often  made  is  for  architects  to  model  auditoriums 
after  those  already  built  that  have  good  acoustical  properties.  It  does 
not  follow  that  halls  so  modeled  will  be  successful,  since  the  materials 
used  in  construction  are  not  the  same  year  after  year.  For  instance, 
a  few  years  ago  it  was  the  usual  custom  to  put  lime  plaster  on  wooden 
lath;  now  it  is  frequently  the  practice  to  put  gypsum  plaster  on  metal 
lath,  which  forms  an  entirely  different  kind  of  a  surface.  This  latter 
arrangement  makes  hard,  non-porous  walls  which  absorb  but  little  sound, 
and  thus  aggravate  the  reverberation.  Further,  a  new  hall  usually 
is  changed  somewhat  in  form  from  the  old  one,  to  suit  the  ideas  of 
the  architect,  and  it  is  very  likely  that  the  changes  will  affect  the 
acoustics. 

1.  Science,  Vol.  35,  p.  833,  1912. 

2.  Arch.   Quarterly  of  Harvard  University.  March,   1912. 


WATSON — ACOUSTICS    OF    AUDITORIUMS  13 

D.       THE  EFFECT  OF  THE   VENTILATION  SYSTEM  ON  THE  ACOUSTICS. 

At  first  thought  it  might  seem  that  the  ventilation  system  in  a  room 
would  affect  the  acoustical  properties.  The  air  is  the  medium  that  trans- 
mits the  sound.  It  has  been  shown  that  the  wind  has  an  action  in 
changing  the  direction  of  propagation  of  sound.1  Sound  is  also  reflected 
and  refracted  at  the  boundary  of  gases  that  differ  in  density  and  tem- 
perature.2 It  is  found,  however,,  that  the  effect  of  the  usual  ventilation 
currents  on  the  acoustics  in  an  auditorium  is  small.  The  temperature 
difference  between  the  heated  currents  and  the  air  in  the  room  is  not 
great  enough  to  affect  the  sound  appreciably,  and  the  motion  of  the 
current  is  too  slow  and  over  too  short  a  distance  to  change  the  action 
of  the  sound  to  any  marked  extent.3 

Under  special  circumstances,  the  heating  and  ventilating  systems 
may  prove  disadvantageous.4  A  hot  stove  or  a  current  of  hot  air  in 
the  center  of  the  room  will  seriously  disturb  the  action  of  sound.  Any 
irregularity  in  the  air  currents  so  that  sheets  of  cold  and  heated  air 
fluctuate  about  the  room  will  also  modify  the  regular  action  of  the  sound 
and  produce  confusion.  The  object  to  be  striven  for  is  to  keep  the  air 
in  the  room  as  homogeneous  and  steady  as  possible.  Hot  stoves,  radia- 
tors, and  currents  of  heated  air  should  be  kept  near  the  walls  and  out 
of  the  center  of  the  room.  It  is  of  some  small  advantage  to  have  the 
ventilation  current  go  in  the  same  direction  that  the  sound  is  to  go, 
since  a  wind  tends  to  carry  the  sound  with  it. 

IV.     THE  INVESTIGATION  IN  THE  AUDITORIUM  AT  THE  UNIVERSITY  OF 

ILLINOIS. 

A.     PRELIMINARY  WORK. 

/ 

As  already  stated,  a  chaos  of  sound  was  set  up  when  an  observer 
in  the  Auditorium  spoke  or  shouted  or  clapped  his  hands.  Both  echoes 
and  reverberations  were  present  and  could  be  heard  in  all  parts  of  the 
room,  though  the  echoes  seemed  to  be  strongest  on  the  stage  and  in  the 
balcony.  The  propects  for  bettering  the  acoustics  were  not  very  encour- 
aging. Luckily,  the  cure  for  the  reverberation  was  fairly  simple,  since 
Sabine's  method  gave  a  definite  procedure  that  could  be  applied  to  this 
case.  The  cure  for  the  echo,  however,  was  yet  to  be  found.  It  was  first 
necessary  to  find  out  which  walls  set  up  the  defect. 


1.  Osborne  Reynolds.     Proc.   of  Royal   Soc..  Vol.   XXII.  p.   531.   1874. 

2.  Joseph  Henry,   "Report  of  the  Lighthouse   Board  of  the  United   States   for  the   year 
1874." 

J.  Tyndall,   Phil.   Trans..   1874. 

3.  Sabine,    Engineering    Record,    Vol.    61,    p.    779,    1910. 
Watson,    Engineering   Record,   Vol.    67.   p.   26f>.    1913. 

4.  Sabine   and    Watson.     Ibid. 


14  ILLINOIS    ENGINEERING    EXPERIMENT   STATION 

The  attempt  to  locate  echoes  by  generating  a  sound  and  listening 
with  the  ear  met  with  only  partial  success.  The  ear  is  sensitive  enough, 
but  becomes  confused  when  many  echoes  are  present,  coming  apparently 
from  every  direction,  so  that  the  evidence  thus  obtained  is  not  altogether 
conclusive.  It  became  apparent  that  the  successful  solution  lay  in  fixing 
the  attention  on  the  sound  going  in  a  particular  direction  -and  finding 
out  where  it  went  after  reflection ;  then  tracing  out  the  path  in  another 
particular  direction,  and  so  on,  until  the  evidence  obtained  gave  some 
hint  of  the  general  action  of  the  sound. 


•> 
FIG.  4.     WATCH  AS  SOURCE  OF  SOUND,  BACKED  BY  A  CONCAVE  REFLECTOR. 


The  first  step  in  the  application  of  this  principle  was  to  use  a 
faint  sound  which  could  not  be  heard  at  any  great  distance  unless  rein- 
forced in  some  way.  The  ticks  of  a  watch  were  directed,  by  means  of 
a  reflector  (Fig.  4)  to  certain  walls  suspected  of  giving  echoes.  Using 
the  relation  that  the  angle  of  incidence  equals  the  angle  of  reflection, 
the  reflected  sound  was  readily  located,  and  the  watch  ticks  heard  dis- 
tinctly after  they  had  traveled  a  total  distance  as  great  as  70  to  80  feet 
from  the  source. 

In  a  later  experiment,  a  metronome  was  used  which  gave  a  louder 
sound.  It  was  enclosed  in  a  sound-proof  structure  (Fig.  5)  with  only 
one  opening,  so  that  the  sound  could  be  directed  by  means  of  a  horn. 
This  method  was  suggested  by  the  work  of  Gustav  Lyon  in  the  Hall  of 
the  Trocadero  at  Paris,*  where  a  somewhat  similar  arrangement  was 
used.  The  method  was  successful  and  verified  the  observations  taken 
previously. 

rLa    Nature    (Paris),   April   24,    1909. 


WATSON ACOUSTICS    OF    AUDITORIUMS 

SOUND  PROOF  BOX 


15 


FIG.  5.      METRONOME  AS  SOURCE  OF  SOUND. 

Though  the  results  obtained  with  the  watch  and  metronome  seemed 
conclusive,  yet  the  observer  was  not  always  confident  of  the  results. 
A  further  method  was  sought,  and  a  more  satisfactory  one  found  by 
using  an  alternating  current  arc-light  at  the  focus  of  a  parabolic  re- 
flector (Fig.  6).  In  addition  to  the  light,  the  arc  gave  forth  a  hissing 
sound,  which  was  of  short  wave  length  and  therefore  experienced  but 
little  diffraction.  The  bundle  of  light  rays  was,  therefore,  accompanied 
by  a  bundle  of  sound,  both  coming  from  the  same  source  and  subject. 


FIG.  6.      ARC-LIGHT  AS  SOURCE  OF  SOUND. 

to  the  same  law  of  reflection.  The  path  of  the  sound  was  easily  found 
by  noting  the  position  of  the  spot  of  light  on  the  wall.  The  reflected 
sound  was  located  by  applying  the  relation  that  the  angles  of  inci- 
dence and  reflection  are  equal.  The  arc-light  sound  was  intense  and 
gave  the  observer  confidence  in  results  that  was  lacking  in  the  other 


16  ILLINOIS    ENGINEERING    EXPERIMENT    STATION 

methods.  To  trace  succcessive  reflections,  small  mirrors  were  fastened 
to  the  reflecting  walls  so  that  the  path  of  the  reflected  sound  was  indi- 
cated by  the  reflected  light.  A  "diagnosis"  of  the  acoustical  troubles  of 
the  Auditorium  was  then  made  by  this  method. 

It  should  be  noted  here  that  the  arc-light  sound  is  not  the  same 
as  the  sounds  of  music  or  speech,  these  latter  ones  being  of  lower  pitch 
and  of  longer  wave  length.  It  was,  therefore,  a  matter  of  doubt  whether 
the  results  obtained  would  hold  also  for  the  case  of  speech  or  music. 
Tests  made  by  observers  stationed  in  the  Auditorium  when  musical  num- 
bers and  speeches  were  rendered,  however,  verified  the  general  conclusions 
obtained  with  the  arc-light. 

It  should  be  pointed  out  in  this  connection  that  there  is  an  objection 
to  applying  the  "ray"  method  of  geometrical  optics  to  the  case  of  sound. 
It  is  much  more  difficult  to  get  a  ray  of  sound  than  it  is  to  get  a  ray  of 
light.*  This  is  due  to  the  difference  in  the  wave  lengths  in  the  two 
cases.  It  appears  that  the  waves  are  diffracted,  or  spread  out,  in  propor- 
tion to  their  length,  the  longer  waves  being  spread  out  to  a  greater 
extent.  The  short  waves  of  light  from  the  sun,  for  instance,  as  they 
come  through  a  window  mark  out  a  sharp  pattern  on  the  floor,  which 
shows  that  the  waves  proceed  in  straight  lines  with  but  little  diffraction 
or  spreading.  Far  different  is  it  with  the  longer  waves  of  sound.  If 
the  window  is  open,  we  are  able  to  hear  practically  all  the  sounds  from 
outdoors,  even  that  of  a  wagon  around  the  corner,  although  we  may  be 
at  the  other  end  of  the  room  away  from  the  window.  The  longer  sound 
waves  spread  out  and  bend  at  right  angles  around  corners,  so  that  it  is 
almost  impossible  to  get  a  sound  shadow  with  them.  Furthermore,  in 
the  matter  of  reflection,  it  appears  that  the  area  of  the  reflecting  wall 
must  be  comparable  with  the  length  of  the  waves  being  reflected.  In 
the  case  of  light,  the  waves  are  very  minute,  hence  a  mirror  can  be  very 
small  and  yet  be  able  to  set  up  a  reflection ;  but  sound  waves  are  of  greater 
1-ength,  the  average  wave  length  of  speech  (45  cm.)  being  about  700000 
times  longer  than  the  wave  length  of  yellow  light  (.00006  cm.),  hence 
the  reflecting  surface  must  be  correspondingly  larger.  An  illustration 
will  perhaps  make  this  clearer.  Suppose  a  post  one  foot  square  projects 
through  a  water  surface.  The  small  ripples  on  the  water  will  be  reflected 
easily  from  the  post,  but  the  large  water  waves  pass  by  almost  as  if  the 
post  were  not  there.  The  reflecting  surface  must  have  an  area  com- 
parable with  the  size  of  the  wave  if  it  is  to  cause  an  effective  reflection. 
Eelief  work  in  auditoriums,  if  of  small  dimensions,  will  affect  only  the 
high  pitched  sounds,  i.  e.,  those  of  short  wave  length,  while  the  low 


*Rayleigh,   "Theory   of   Sound,"   Vol.   II,   §    283. 


WATSON — ACOUSTICS    OF    AUDITORIUMS 


17 


pitched  sounds  of  long  wave  length  are  reflected  much  the  same  as  from 
a  rather  rough  wall.  It  is  also  shown  that  the  area  of  the  reflecting 
surface  is  dependent  on  its  distance  from  the  source  of  sound  and  from  the 
observer ;  the  greater  these  distances  are  the  larger  must  be  the  reflecting 
surface.* 

These  considerations  all  show  that  the  reflection  of  sound  is  a  com- 
plicated matter.  The  dimensions  of  a  wall  to  reflect  sound,  or  of  relief 
work  to  scatter  it,  are  determined  by  the  wave  length  and  by  the  various 
other  factors  mentioned.  It  should  be  said  with  caution  that  a  "ray" 
of  sound  is  reflected  in  a  definite  way  from  a  small  bit  of  relief  work. 
We  must  deal  with  bundles  of  sound,  not  too  sharply  bounded,  and  have 
them  strike  surfaces  of  considerable  area  in  order  to  produce  reflections 
with  any  completeness. 


FIG.  7.    LONGITUDINAL  SECTION  SHOWING  THE  CHIEF  CONCENTRATIONS  OF  SOUND, 
THE  DIFFRACTION  EFFECTS  BEING  DISREGARDED. 


B.       DETAILS  OF  THE  ACOUSTICAL  SURVEY  IN  THE  AUDITORIUM. 

The  general  effect  of  the  walls  of  the  Auditorium  on  the  sound  may 
be  anticipated  by  considering  analogous  cases  in  geometrical  optics,  but 
with  the  restrictions  on  "rays"  described  in  the  preceding  paragraph. 
The  sound  does  not  actually  confine  itself  to  the  sharp  boundaries  shown. 
The  diagrams  are  intended  to  indicate  the  main  effect  of  the  sound  in 
the  region  so  bounded.  Pig.  7  gives  such  an  idea  for  the  concentration 
of  sound  in  the  longitudinal  section  of  the  Auditorium. 

*Rayleigh,   ibid.,   283. 


18 


ILLINOIS    ENGINEERING    EXPERIMENT    STATION 


The  plan  followed  in  the  experimental  work  was  to  anticipate  the 
path  of  the  sound  as  indicated  in  Fig.  7,  then  to  verify  the  results  with 
the  arc-light  reflector.  Figs.  8  and  9  show  the  effect  of  the  rear  wall 
in  the  balcony  in  forming  echoes  on  the  stage.  The  speaker  was  particu- 
larly unfortunate,,  being  afflicted  with  no  less  than  ten  echoes. 


FIG.  8. 


LONGITUDINAL  SECTION  SHOWING    How    SOUND    Is 
STAGE  TO  FORM  AN  ECHO. 


RETURNED    TO    THE 


FIG,  9.    LONGITUDINAL  SECTION   SHOWING  FORMATION  OF  ECHO  ON  THE  STAGE. 

The  hard,  smooth,  circular  wall  bounding  the  main  door  under  the 
balcony  gave  echoes  as  shown  in  Fig.  10,  the  sound  going  also  in  the 
reverse  direction  of  the  arrows. 


WATSON — ACOUSTICS    OF    AUDITORIUMS 

— Vk  L~- — ^ 


19 


FIG.  10.     PLAN  OF  AUDITORIUM  SHOWING  ACTION  OF  REAR  WALL  ON  THE  SOUND. 


FLOOR.  PLAN 

FIG.    11.     PLAN   OF   AUDITORIUM    SHOWING   CONCENTRATION   OF   SOUND   BY   THE 

REAR  WALL. 


ILLINOIS    ENGINEERING    EXPERIMENT    STATION 


FlG.  12. 


THIS  FIGURE  TAKEN  WITH  FIG.  9  SHOWS  How  AN  ECHO  Is  SET  UP  ON 
THE  STAGE. 


A  more  comprehensive  idea  of  the  action  of  this  wall  is  shown  in 
Fig.  11.  This  reflected  sound  was  small  in  amount  and  therefore  not 
a  serious  disadvantage. 

The  cases  cited  were  fairly  easy  to  determine  since  the  bundles  of 
sound  considered  were  confined  closely  to  either  a  vertical  or  a  horizontal 
plane  for  which  the  plans  of  the  building  gave  some  idea  of  the  probable 
path  of  the  sound.  For  other  planes,  the  paths  followed  could  be  antici- 
pated by  analogy  from  the  results  already  found.  Fig.  12  shows  in 
perspective  the  development  of  the  result  expressed  in  Fig.  9. 

A  square  bundle  of  sound  starts  from  the  stage  and  strikes  the 
spherical  surface  of  the  dome.  After  reflection,  it  is  brought  to  a  point 
focus,  as  shown,  and  spreads  out  until  it  strikes  the  vertical  cylindrical 
wall  in  the  rear  of  the  balcony.  This  wall  reflects  it  to  a  line  focus, 
after  which  it  proceeds  to  the  stage.  Auditors  on  all  parts  of  the  stage 
complained  of  hearing  echoes. 


WATSON — ACOUSTICS    OF    AUDITORIUMS  21 

Referring  to  Fig.  7,  it  is  seen  that  the  arch  over  the  stage  reflects 
sound  back  to  the  stage.  Fig.  13  shows  in  perspective  the  focusing 
action  of  this  overhead  arch.  Fig.  14  shows  the  effect  of  the  second  arch. 


FIG.  13.     PERSPECTIVE  OF  STAGE  SHOWING  FOCUSING  ACTION  OF  ARCH  ON  SOUND. 

Some  of  this  sound  is  reflected  to  the  stage  and  to  the  seats  in  front  of 
the  stage ;  other  portions,  striking  more  nearly  horizontally,  are  reflected 
to  the  side  balconies.  The  echoes  are  not  strong  except  for  high  pitched 
notes  with  short  wave  lengths,  since  the  width  of  the  arch  is  small. 

Passing  now  to  the  transverse  section,  Fig.  15,  we  find  the  most 
pronounced  echoes  in  the  Auditorium.  If  an  observer  generates  a  sound 
in  the  middle  of  the  room  directly  under  the  center  of  the  skylight, 
distinct  echoes  are  set  up.  A  bundle  of  sound  passes  to  the  concave  sur- 
face which  converges  the  sound  to  a  focus,  after  which  it  spreads  out 
again  to  the  other  concave  surface  and  is  again  converged  to  a  focus 


ILLINOIS    ENGINEERING    EXPERIMENT    STATION 


FIG.   14.     PERSPECTIVE  OF   STAGE  SHOWING  FOCUSING  ACTION  OF   SECOND  ARCH. 


FIG.  15.    TRANSVERSE  SECTION   SHOWING  HOW  MOST  PRONOUNCED  ECHOES  ARE 
SET  UP  BY  THE  Two  CONCAVE  SURFACES. 


WATSON ACOUSTICS    OF    AUDITORIUMS  23 

nearly  at  the  starting  point.  The  distance  traveled  is  about  225  feet, 
taking  about  *4  second,  so  that  the  conditions  are  right  for  setting  up 
a  strong  echo.  This  echo  is  duplicated  by  the  sound  which  goes  in  the 
reverse  of  the  path  just  described.  Another  echo,  somewhat  less  strong, 
is  formed  by  the  sound  that  goes  to  the  dome  overhead  and  which  is 
reflected  almost  straight  back,  since  the  observer  is  nearly  at  the  center 
of  the  sphere  of  which  the  dome  is  a  part.  These  echoes  repeat  them- 
selves, for  the  sound  does  not  stop  on  reaching  the  starting  point,  but 
is  reflected  from  the  floor  and  repeats  the  action  just  described.  As 
many  as  ten  distinct  echoes  have  been  generated  by  a  single  impulse 
of  sound. 


FIG.  16.     ACTION  OF  SOUND  IN  CAUSING  ECHO  ON  THE  STAGE. 

The  echo  shown  in  Fig.  15  is  repeated  in  a  somewhat  modified  form 
for  a  sound  generated  on  the  stage  by  a  speaker.  Fig.  16  shows  the 
path  taken  by  the  sound.  This  echo  is  duplicated  by  the  sound  that 
goes  in  the  reverse  direction  of  the  arrows,  so  the  speaker  is  greeted  from 


24  ILLINOIS    ENGINEERING   EXPERIMENT   STATION 

both  sides.  Fig.  17  is  a  perspective  showing  the  path.  The  sound  does 
not  confine  itself  closely  to  a  geometrical  pattern,,  as  shown  in  the  picture, 
but  spreads  out  by  diffraction.  The  main  effect  is  shown  by  the  figure. 


FIG.   17.     PERSPECTIVE  SHOWING  HOW  AN  ECHO  Is   FORMED  ON  THE  STAGE  BY 

Two  REFLECTIONS.    DIFFRACTION  EFFECTS  ARE  NOT  CONSIDERED 

IN  THIS  DRAWING. 

Thus  far  only  the  echoes  that  reached  the  stage  have  been  described. 
Other  echoes  were  found  in  other  parts  of  the  hall,  and  it  seemed  that 
few  places  were  free  from  them.  The  side  walls  in  the  balcony,  for 
instance,  were  instrumental  in  causing  strong  echoes  in  the  rear  of  the 
balcony.  Fig.  18  shows  in  perspective  the  action  of  one  of  these  walls. 
These  two  surfaces  were  similar  in  shape  and  symmetrically  placed. 
Each  was  the  upper  portion  of  a  concave  surface  with  its  center  of 
curvature  in  the  center  of  the  building  under  the  dome.  The  general 
effect  of  the  left  hand  wall  was  to  concentrate  the  sound  falling  on  it 


WATSON ACOUSTICS    OE    AUDITORIUMS  25 

in  the  right  hand  seats  in  the  balcony.  Some  of  the  sound  struck  the 
opposite  wall  and  was  reflected  to  the  stage,  as  shown  in  Fig.  17.  Audi- 
tors who  sought  the  furthermost  rear  seats  in  the  balcony  to  escape  echoes 
were  thus  caught  by  this  unexpected  action  of  the  sound.  The  right 
hand  wall  acted  in  a  similar  way  to  send  the  sound  to  the  upper  left 
balcony. 


FIG.    18.     PERSPECTIVE    SHOWING    SOUND    REFLECTOR   FROM    CONCAVE    WALL    IN 
BALCONY.     DIFFRACTION  NOT  CONSIDERED. 


The  dome  surface  concentrates  most  of  its  sound  near  the  front 
of  the  central  portion  of  the  balcony  and  the  ground  floor  in  front  of 
the  .balcony  in  the  form  of  a  caustic  cone.  Figs.  7,  9  and  11  give  some 
conception  of  how  a  concentration  of  sound  is  caused  by  this  spherical 
surface.  The  echo  in  the  front  portion  of  the  balcony  was  especially 
distinct.  On  one  occasion,  in  this  place,  the  author  was  able  to  hear  the 
speaker  more  clearly  torn  the  echo  than  by  listening  to  the  direct  sound. 


26  ILLINOIS    ENGINEERING    EXPERIMENT    STATION 

Minor  echoes  were  set  up  by  the  horizontal  arch  surfaces  in  the 
balcony.  The  sound  from  the  stage  was  concentrated  by  reflection  from 
these  surfaces  and  then  passed  to  a  second  reflection  from  the  concave 
surfaces  back  of  them.  Auditors  in  the  side  balcon}r  were  thus  disagree- 
ably startled  by  having  the  sound  come  from  overhead  from  the  rear. 

C.       CONCLUSION  DRAWN  FROM  THE  ACOUSTICAL  SURVEY. 

The  results  of  the  survey  show  that  curved  walls  are  largely  respon- 
sible for  the  formation  of  echoes  because  they  concentrate  the  reflected 
sound.  It  seems  desirable,  therefore,  to  emphasize  the  danger  of  using 
such  walls  unless  their  action  is  annulled  by  absorbing  materials  or  relief 
work.  Large  halls  with  curved  walls  are  almost  sure  to  have  acoustical 
defects. 

D.       METHODS    EMPLOYED   TO    IMPROVE   THE  ACOUSTICS. 

Reflecting  Boards. — The  provisional  cure  was  brought  about  grad- 
ually by  trying  different  devices  suggested  by  the  diagnosis.  In  one  set 
of  experiments  sounding  boards  of  various  shapes  and  sizes  were  used. 
A  flat  board  about  five  feet  square  placed  at  an  incline  over  the  position 
of  the  speaker  produced  little  effect  A  larger  canvas  surface,  about 
12  by  20  feet,  was  not  much  better.  A  parabolic  reflector,  however, 
gave  a  pronounced  effect.  This  reflector  was  mounted  over  a  pulpit  at 
one  end  of  the  stage  and  served  to  intercept  much  of  the  sound  that 
otherwise  would  have  gone  to  the  dome  and  produced  echoes.  The 
path  of  the  reflected  sound  was  parallel  to  the  axis  of  the  paraboloid  of 
which  the  reflector  was  a  quarter  section.  There  was  no  difficulty  in 
tracing  out  the  reflected  sound.  Auditors  in  the  path  of  the  reflected 
rays  reported  an  echo,  but  auditors  in  other  parts  of  the  Auditorium 
were  remarkably  free  from  the  usual  troubles.  The  device  was  not  used 
permanently,  since  many  speakers  objected  to  the  raised  platform.  More- 
over, it  was  not  a  complete  cure,  since  it  was  not  suited  for  band  con- 
certs and  other  events,  where  the  entire  stage  was  used.  Another  reflector 
similar  in  shape  to  the  one  just  described  is  shown  in  Figs.  21  and  22. 

Sabine's  Method. — The  time  of  reverberation  was  determined  by 
Sabine's  method.  An  organ  pipe  making  approximately  526  vibrations 
a  second  was  blown  for  about  three  seconds  and  then  stopped.  An 
auditor  listened  to  the  decreasing  sound,  and  when  it  died  out  made 
a  record  electrically  on  a  chronograph  drum.  The  time  of  reverberation 
was  found  to  be  5.90  seconds,  this  being  the  mean  of  19  sets  of  measure- 
ments, each  of  about  20  observations.  The  reverberation  was  found  also 
by  calculation  from  Sabine's  equation  (see  Section  III),  taking  the 
volume  of  the  Auditorium  as  11  800  cubic  meters  and  calculating  the 


WATSON ACOUSTICS    OF    AUDITORIUMS 


FIG.  19.     REFLECTING  BOARD  IN  PROCESS  OF  CONSTRUCTION. 


FIG.  20.    FINISHED  REFLECTOR.     HARD  PLASTER  ON  WIRE  LATH. 


ILLINOIS    ENGINEERING    EXPERIMENT    STATION 


FIG.  21.     PARABOLIC  REFLECTOR  SHOWING  ITS  ACTION  ON  SOUND. 


FIG.  22.     PHOTOGRAPH  OF  PARABOLIC  REFLECTOR. 


WATSON — ACOUSTICS    OF    AUDITORIUMS  29 

absorbing  power  of  all  the  surfaces  in  the  room.  This  calculation  gave 
6.4  seconds.  The  agreement  between  the  two  results  is  as  close  as 
could  be  expected,  since  neither  the  intensity  of  the  sound  nor  the 
pitch  used  by  the  author  was  the  same  as  those  used  by  Professor  Sabine, 
and  both  of  these  factors  affect  the  time  of  reverberation. 

Several  years  later  the  time  of  reverberation  was  again  determined 
after  certain  changes  had  been  made.  A  thick  carpet  had  been  placed 
on  the  stage,  heavy  velour  curtains  18  by  32  feet  in  area  hung  on  the 
wall  at  the  rear  of  the  stage,  a  large  canvas  painting  400  square  feet  in 
area  was  installed,  and  the  glass  removed  from  the  skylight  in  the  ceiling. 
The  time  of  reverberation  was  reduced  to  4.8  seconds.  With  an  audience 
present  this  value  was  reduced  still  more,  and  when  the  hall  was 
crowded  at  commencement  time  the  reverberation  was  not  troublesome. 

Method  of  Eliminating  Echoes. — Although  the  time  of  reverberation 
was  reduced  to  be  fairly  satisfactory,  as  just  explained,  the  echoes  still 
persisted,  and  were  very  annoying.  Attempts  were  made  to  reduce 
individual  echoes  by  hanging  cotton  flannel  on  the  walls  at  critical 
points.  Thus  the  shaded  areas  in  Fig.  17  were  covered  and  also  the 
entire  rear  wall  in  the  balcony.  Pronounced  echoes  still  remained,  and 
it  was  evident  that  some  drastic  action  was  necessary  to  alleviate  this 
condition.  Four  large  canvases,  shown  in  Figs.  23  and  24,  were  then 
hung  in  the  dome  in  position  suggested  by  the  results  of  the  diagnosis. 
A  very  decided  improvement  followed.  For  the  first  time  the  echoes 
were  reduced  to  a  marked  degree  and  speakers  on  the  stage  could  talk 
without  the  usual  annoyance.  This  arrangement  eliminated  the  echoes 
not  only  on  the  stage,  but  generally  all  over  the  house.  A  number  of 
minor  echoes  were  still  left,  but  the  conditions  were  much  improved, 
especially  when  a  large  audience  was  present  to  reduce  the  reverberation. 

Proposed  Final  Cure. — The  state  of  affairs  just  described  is  the 
condition  at  the  time  of  writing.  Two  propositions  were  considered  in 
planning  the  final  cure.  One  proposition  involved  a  complete  remodeling 
of  the  interior  of  the  Auditorium.  Plans  of  an  interior  were  drawn  in 
accordance  with  the  results  of  the  experimental  work  that  would  probably 
give  satisfactory  acoustics.  This  proposition  was  not  carried  out  because 
of  the  expense  and  because  it  was  thought  desirable  to  attempt  a  cure 
without  changing  the  shape  of  the  room.  The  latter  plan  is  the  one 
now  being  followed.  It  is  proposed  to  replace  the  present  unsightly 
curtains  with  materials  which  will  conform  to  the  architectural  features 
of  the  Auditorium  and  which  will  have  a  pleasing  color  scheme.  At 
the  same  time,  it  will  be  necessary  to  hold  to  the  features  which  have 
improved  the  acoustics. 


30  ILLINOIS    ENGINEERING   EXPERIMENT   STATION 


FIG.  23.     PHOTOGRAPH  OF  Two  OF  THE  CANVAS  CURTAINS  IN  THE  DOME  OF  THE 
AUDITORIUM.     NOTE  ALSO  THE  ABSORBING  MATERIALS  UNDER  THE  ARCHES. 


FIG.   24.     PHOTOGRAPH  OF  DOME  OF  AUDITORIUM   SHOWING  THE  CANVASES  IN- 
STALLED TO  ELIMINATE  ECHOES. 


WATSON — ACOUSTICS   OF  AUDITORIUMS  31 


encyclopaedia   of  acoustics,   the   following  topics  applying  to   the  subject  in   hand:     "Akustik 
der  Gebaude,"  pp.   580-584,  with  references.     "Nachhall  und  Echo,"  pp.  565-569,  with 


V.     BIBLIOGRAPHY  OF  PUBLICATIONS  ON  ACOUSTICS  OF  AUDITORIUMS. 

Auerbach,  F.  "Akustik."  Winkelmann's  Handbuch  der  Physik,  Vol.  II,  1909.  An 

" :  "Akmtik 
with  refer- 
ences. 

Blackall,  C.  H.  "Acoustics  of  Audience  Halls,"  Engineering  Record,  Vol.  45,  pp.  541- 
542,  1902.  A  paper  recording  the  opinions  of  the  author  with  many  references  to  acoustical 
properties  of  particular  audience  halls. 

Cornelison,  R.  W.  "The  Acoustical  Properties  of  Rooms  Particularly  as  Affected  by 
Wall  Coverings,"  1905.  A  pamphlet  describing  the  merits  of  "Fabrikona"  burlap  as  a  sound 
absorber.  H.  B.  Wiggin's  Sons  Company,  Bloomfield,  N.  J. 

Eichhorn,  A.  "Die  Akustik  Grosser  Raume  nach  Altgriechischer  Theorie."  Ernst  and 
Korn,  Publishers,  Berlin,  1888.  A  discussion  of  Greek  buildings  and  acoustics,  with  appli- 
cations to  modern  conditions. 

Eichhorn,  A.  "Der  Akustische  Masstab  fur  die  Projectbearbeitung  Grosser  Innen 
Raume."  Published  by  Schuster  and  Bufleb,  Berlin,  1899.  A  continuation  of  the  previous 
work. 

Exner,  S.  "Uber  die  Akustik  von  Horsalen  und  ein  Instrument,  sie  zu  bestimmen." 
Zeitschrift  des  Osterreichischen  Ingenieur  und  Architekten-Vereines,  Vol.  LVII,  p.  141, 
March,  1905.  Indicates  his  opinion  of  good  acoustical  properties  in  a  hail.  Gives  experi- 
mental determination  of  reverberation. 

Fournier,  Lucien.  "The  Suppression  of  Echoes."  La  Nature  (Paris),  April  24,  1909. 
English  translation  given  in  "The  Literary  Digest,"  New  York,  May  29,  1909,  p.  924.  An 
account  of  the  experiments  of  Gustav  Lyon  in  investigating  the  echoes  in  Trocadero  Hall 
in  Paris. 

Franklin,  W.  S.  "Derivation  of  Equation  of  Decaying  Sound  in  a  Room  and  Defini- 
tion of  Open  Window  Equivalent  of  Absorbing  Power."  Physical  Review,  Vol.  16,  pp. 
372-374,  1903.  A  theoretical  development  of  the  formula  found  experimentally  by  Sabine. 

Haege.  "Bemerkungen  fiber  Akvstik."  Zeitschrift  fur  Baumesen,  Vol.  IX,  pp.  582- 
594, 1859. 

Henry,  Joseph.  "Acoustics  Applied  to  Public  Buildings,"  Smithsonian  Report,  1856, 
p.  221. 

Hoyt,  J.  T.  N.  "The  Acoustics  of  the  Hill  Memorial  Hall,"  American  Architect,  Vol. 
CIV,  pp.  50-53,  August  6,  1913.  Discusses  the  design  of  the  hall  and  indicates  how  it  ful- 
fills his  ideas  of  good  acoustics. 

Hutton,  W.  R.  "Architectural  Acoustics;  Hall  of  Representatives,  U.  S.  Capitol,  1858." 
Engineering  Record,  Vol.  42,  p.  377,  1900.  A  discussion  of  the  cure  of  the  faulty  acoustics 
in  the  U.  S.  Hall  of  Representatives. 

Jacques,  W.  W.  "Effect  of  the  Motion  of  the  Air  Within  an  Auditorium  Upon  Its 
Acoustical  Qualities."  Philosophical  Magazine  (5),  Vol.  7,  p.  Ill,  1879.  A  record  of 
experiments  in  the  Baltimore  Academy  of  Music  showing  that  the  ventilating  current  had  a 
marked  action  on  the  acoustics. 

Jager,  S.  "Zur  Theorie  des  Nachhals,"  Sitzungsberichten  der  Kaiserl.  Akademie  der 
Wissenschaften  in  Wien.  Matem.-naturw.  Klasse;  Bd.  CXX,  Abt.  Ha,  Mai,  1911.  An 
important  paper  giving  a  theoretical  development  of  Sabine's  formula  showing  the  factors 
that  enter  into  the  constants.  Considers  also  the  case  of  the  reflection  of  sound  from  a 
thin  wall  and  also  the  case  when  it  encounters  a  porous  material  such  as  a  curtain. 

Lamb,  Horace.  "The  Dynamical  Theory  of  Sound."  Published  by  Edward  Arnold, 
London,  1910.  A  more  elementary  treatment  than  Rayleigh's  "Theory  of  Sound." 

Marage.  "Qualites  acoustiques  de  certaines  sailes  pour  la  voix  parlee."  Comptes 
Rendus,  Vol.  142,  p.  878,  1906.  An  investigation  of  the  acoustical  properties  of  six  halls 
in  Paris. 

Norton,  C.  L.  "Soundproof  Partitions."  Insurance  Engineering,  Vol.  4,  p.  180,  1902. 
An  account  of  experimental  tests  of  the  soundproof  qu'alities  of  materials  that  are  also 
fireproof. 

Orth,  A.  "Die  Akustik  Grosser  Raume  mit  Speciallem  Bezug  auf  Kirchen."  Zeitschrift 
fur  Bauwesen.  Also  reprint  by  Ernst  and  Korn,  Berlin,  1872.  Assumes  that  sound 
waves  behave  like  light  waves.  Discusses,  with  detailed  drawings,  the  paths  of  sound  in 
the  Zion  Church  in  Berlin  and  the  Nicolai  Church  in  Potsdam.  Also  gives  his  opinion  of  the 
effect  of  surfaces  and  materials  on  sound. 

Rayleigh,  Lord.  "Theory  of  Sound."  Two  volumes,  Macmillan,  1896.  The  unsur- 
passed classic  in  the  subject  of  acoustics.  References  to  architectural  acoustics  as  follows: 
"Whispering  Galleries,"  Vol.  II,  §  287.  "Passage  of  Sound  Through  Fabrics,"  Vol.  II, 
p.  811.  "Resonance  in  Buildings,"  Vol.  II,  §  252. 

Sabine,  Wallace  C.  "Architectural  Acoustics."  Engineering  Record,  1900,  Vol.  1,  pp. 
349,  876,  400,  426,  450,  477,  503.  Published  also  in  book  form  and  in  American  Architect, 
Vol.  68,  1900,  pp.  3,  19,  35,  43,  59,  75,  83.  An  important  series  of  articles  giving  the 
relation  between  the  time  of  reverberation  in  a  room,  the  volume  of  the  room,  and  absorb- 
ing materials  present.  Gives  table  of  absorbing  powers  of  substances,  so  that  an  archi- 
tect can  calculate  in  advance  of  construction  what  the  time  of  reverberation  will  be. 


32  ILLINOIS  ENGINEERING  EXPERIMENT  STATION 

Sabine,  W.  C.  "Architectural  Acoustics,"  Proc.  of  the  Amer.  Acad.  of  Arts  and 
Sciences,  Vol.  XLII,  No.  2,  June,  1906.  A  continuation  of  the  previous  work,  showing  the 
accuracy  of  musical  taste  in  regard  to  architectural  acoustics  and  also  the  variation  in 
reverberation  with  variation  in  pitch. 

Sabine,  W.  C.  "Architectural  Acoustics,"  Engineering  Record,  Vol.  61,  pp.  779-781,  June 
18,  1910.  Discusses  the  case  of  flow  of  air  in  a  room  and  its  effect  on  the  acoustics.  Con- 
cludes that  the  usual  ventilation  system  in  a  hall  has  very  little  effect. 

Sabine,  W.  C.  "Architectural  Acoustics:  The  Correction  of  Acoustical  Difficulties." 
The  Architectural  Quarterly  of  Harvard  University,  March,  1912,  pp.  3-23.  An  account 
of  the  cures  of  the  acoustical  difficulties  of  a  number  of  audience  rooms,  also  a  description 
of  further  experiments  on  the  absorbing  power  of  different  materials. 

Sabine,  W.  C.  "Theater  Acoustics."  American  Architect,  Vol.  CIV,  pp.  257-279,  Decem- 
ber 31,  1913.  Describes  theater  with  model  acoustics.  Discusses  behavior  of  sound  in  a 
room  and  shows  photographs  of  sound  waves  in  miniature  rooms. 

Sabine,  W.  C.  "Architectural  Acoustics.  Building  Material  and  Musical  Pitch."  The 
Brickbuilder,  Vol.  23,  pp.  1-6,  January,  1914.  A  continuation  of  previous  work,  describing 
absorbing  powers  of  different  materials. 

Sharpe,  H.  J.  "Reflection  of  Sound  at  a  Paraboloid."  Camb.  Phil.  Soc.  Proc.,  Vol. 
15,  pp.  190-197,  1909. 

Stewart,  G.  W.  "Architectural  Acoustics."  Sibley  Journal  of  Engineering,  May,  1903. 
Published  by  Cornell  University,  Ithaca,  N.  Y.  An  account  of  an  investigation  leading  to 
the  cure  of  the  acoustics  of  Sibley  Auditorium. 

Sturmhofel,  A.  "Akustik  des  Baumeisters."  Published  by  Schuster  and  Bufleb,  Ber- 
lin, 1894.  An  87-page  pamphlet  on  the  acoustics  of  rooms.  Discusses  effects  of  relief  work 
in  rooms  on  sound.  Account  of  experimental  work.  References  to  auditoriums. 

Tallant,  Hugh.  "Hints  on  Architectural  Acoustics."  The  Brickbuilder,  Vol.  19,  1910, 
pp.  Ill,  155,  199,  243,  265.  A  series  of  articles  giving  an  exposition  of  the  principles  of 
the  subject  with  practical  applications. 

Tallant,  Hugh.  "Acoustical  Design  in  the  Hill  Memorial  Auditorium,  University  of 
Michigan."  The  Brickbuilder,  Vol.  XXII,  p.  169,  August,  1913.  See  also  plates  113,  114, 
115.  A  discussion  of  the  acoustical  results  obtained  in  this  auditorium,  a  special  feature 
being  the  action  of  a  huge  parabolic  reflecting  wall  surface  over  the  stage. 

Tallant,  Hugh.  "Architectural  Acoustics.  The  Effect  of  a  Speaker's  Voice  in  Different 
Directions."  The  Brickbuilder,  Vol.  22,  p.  225,  October,  1913. 

Taylor,  H.  O.  "A  Direct  Method  of  Finding  the  Value  of  Materials  as  Sound  Ab- 
sorbers." Physical  Review,  Vol.  2  (2),  p.  270,  October,  1913. 

Tufts,  F.  L.  "Transmission  of  Sound  Through  Porous  Materials."  Amer.  Journal 
of  Science,  Vol.  II,  p.  357,  1901.  Experimental  work  leading  to  the  conclusion  that  sound 
is  transmitted  through  porous  materials  in  the  same  proportion  that  a  current  of  air  is. 

Watson,  F.  R.  "Echoes  in  an  Auditorium."  Physical  Review,  Vol.  32,  p.  231,  1911. 
An  abstract  giving  an  account  of  the  experiments  in  the  auditorium  at  the  University  of 
Illinois. 

Watson,  F.  R.  "Inefficiency  of  Wires  as  a  Means  of  Curing  Defective  Acoustics  of 
Auditoriums."  Science,  Vol.  85,  p.  833,  1912. 

Watson,  F.  R.  "The  Use  of  Sounding  Boards  in  an  Auditorium."  Physical  Review, 
Vol.  1  (2),  p.  241,  1913.  Also  a  more  complete  article  in  The  Brickbuilder,  June,  1913. 

Watson,  F.  R.  "Air  Currents  and  the  Acoustics  of  Auditoriums."  Engineering  Record, 
Vol.  67,  p.  265,  1913.  A  detailed  account  giving  theory  and  experimental  work,  with 
application  to  ventilating  systems  in  auditoriums. 

Watson,  F.  R.  "Acoustical  Effect  of  Fireproofed  Cotton-Flannel  Sound  Absorbers." 
Engineering  News,  Vol.  71,  p.  261,  January  29,  1914.  Results  of  experiments  showing 
that  cotton-flannel  has  practically  the  same  absorbing  power  after  fireproofing  as  before. 

Weisbach,  F.  "Versuche  uber  Schalldurchlassigkeit,  Schallreflexion  und  Schallabsorb- 
tion."  Annalen  der  Physik,  Vol.  33,  p.  763,  1910. 

Williams,  W.  M.  "Echo  in  Albert  Hall."  Nature,  Vol.  3,  p.  469,  1870-71.  Observa- 
tions on  the  shape  of  Albert  Hall  in  London  and  the  echoes  set  up. 

Editorial  Notice.  "The  Dresden  Laboratory  for  Architectural  Acoustics."  American 
Architect,  Vol.  102,  p.  137,  October  16,  1912.  States  that  a  laboratory  of  applied  acoustics 
is  authorized  in  the  Dresden  (Germany)  Technische  Hochschule,  and  that  expert  advice 
will  be  furnished  architects  and  others  regarding  problems  of  acoustics  of  auditoriums. 


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Bulletin  No.  27.  Tests  of  Brick  Columns  and  Terra  Cotta  Block  Columns,  by  Arthur 
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*Bulletin  No.  30.  On  the  Rate  of  Formation  of  Carbon  Monoxide  in  Gas  Producers,  by 
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•Bulletin  No.   47.     Magnetic   Properties   of   Heusler   Alloys,   by    Edward    B.    Stephenson. 

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•Bulletin  No.  60.  The  Coking  of  Coal  at  Low  Temperatures,  with  a  Preliminary  Study 
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[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  Ill,  No.  5,  May,  1914.] 


A  MODIFIED   METHOD  OF  MEASURING  elm  AND  v  FOR 

CATHODE  RAYS. 

BY  L.  T.  JONES. 

THIS  determination  of  elm  and  v  is  a  modification  of  the  usual  method 
employing  the  simultaneous  electrostatic  and  magnetic  deflections. 
The  modification  is  the  result  of  an  attempt  to  eliminate  as  nearly  as 
possible  the  errors  of  measurement  of  the  deflections  and  the  correction 
due  to  the  field  distribution  at  the  ends  of  the  electrostatic  plates.  This 
is  brought  about  chiefly  by  the  position  in  which  the  photographic  plate 
was  placed. 

THE  APPARATUS. 

A  glass  cylinder  10  cm.  in  diameter  and  27  cm.  long  (Fig.  i)  was  closed 
at  each  end  by  a  glass  plate. 
Two  holes  were  made  in 
one  of  the  plates  to  admit 
the  glass  tubes  carrying  the 
anode,  A,  and  the  cathode, 
C.  The  cathode,  an  alum- 
inum disc  .6  cm.  in  diam- 
eter, was  carried  on  an 
aluminum  rod.  This  rod 
was  encased  in  a  small  glass 
tube  which  in  turn  was 
supported  by  a  larger  glass 

tube  waxed  to  the  glass  plate  where  it  entered  the  discharge  chamber. 
The  anode  was  mounted  in  a  similar  manner.  Both  aluminum  rods  were 
connected  with  the  outside  by  platinum  wires  sealed  in  glass. 

A  brass  ring,  D,  was  fastened  by  sealing  wax  to  the  inside  of  the  glass 
cylinder,  and  to  this  were  fastened  the  soft  iron  shield,  S,  and  the  ebonite 
disc,  B,  the  latter  supporting  the  electrostatic  plates.  The  electrostatic 
plates  were  held  to  the  disc  B  by  brass  screws.  The  potential  of  the 
electrostatic  plates  was  supplied  through  two  wires  that  passed  through 
small  holes  in  the  walls  of  the  cylinder.  The  holes  were  sealed  with  wax. 

317 


Fig.  1. 


3l8  L.  T.JONES. 

By  loosening  the  screws  holding  the  ebonite  disc,  B,  to  the  brass  ring, 
D,  the  disc  and  electrostatic  plates  could  be  taken  as  a  whole  from  the 
cylinder. 

At  the  opposite  end  a  short  length  of  brass  cylinder,  G,  was  waxed  to 
the  inside  of  the  glass  cylinder  and  a  hard  rubber  disc,  F,  turned  to  fit 
it,  darkened  the  tube.  The  glass  cylinder  was  coated  on  the  outside 
with  lamp  black  and  the  coating  connected  to  earth.  All  the  metal  parts 
inside  the  tube,  except  the  electrostatic  plates  and  the  discharge  terminals, 
were  connected  to  earth. 

THE  ELECTROSTATIC  PLATES. 

Two  electrostatic  plates  were  mounted  exactly  i  cm.  apart,  as  shown 
in  Fig.  2.     The  beam  of  cathode  rays  was  made  to  pass  along  the  upper 
x^"  of  the  two  plates  at  grazing 

I         incidence.     The  photographic 
J       plate  was  placed  flat  on  the 
.   r\     lower  of  the  two  electrostatic 
plates.     The  beam  was  bent 
downward,  by  adjusting  the 
Fig.  2.  electric    field,    to   strike    the 

photographic  plate  well  with- 
in the  geometrical  limits  of  the  field  plates. 

The  cathode  beam  emerged  from  the  Thomson  plate-tube  at  a  distance 
of  several  centimeters  from  the  left  end  of  the  electrostatic  plates  and 
was  then  bent  downward.  Since  the  plates  were  plane  and  parallel 
the  electrostatic  deflection  was  the  distance  from  the  upper  electrostatic 
plate  to  the  upper  side  of  the  photographic  plate. 

THE  FORMULA. 

Let  the  two  electrostatic  plates  be  separated  by  a  distance  d  -f-  /,  d 
being  the  air  place  and  t  the  thickness  of  the  photographic  plate,  which  is 
of  dielectric  constant  K.  The  two  electrostatic  plates  are  kept  at 
constant  potentials  V  and  V". 

If  the  plates  are  separated  by  an  air  space  of  thickness  d  +  t  there  is  a 
given  electric  surface  density  of  charge  on  the  plates  and,  consequently, 
a  given  electric  force,  E,  in  the  space  between  them.  If,  now,  the  dielec- 
tric of  thickness  /  is  introduced,  whose  equivalent  air  thickness  is  t/K, 
the  effective  air  space  will  then  be  reduced  from  d  +  /  to  d  +  t/K.  The 
effective  air  space  has  thereby  been  reduced  an  air-equivalent  amount  of 
/  —  tjK,  causing  a  change  in  the  capacity.  Since  the  potentials  of  the 
two  plates  have  remained  constant  the  surface  density  and  hence  the 


Nous?1']  METHOD  OF  MEASURING  e/m  AND  v.  319 

electric  force  have  changed.  If,  now,  the  air  gap  between  the  two 
electrostatic  plates  is  increased  by  an  amount  t  —  t/K,  then  the  capacity, 
the  surface  density  and  the  electric  force  will  resume  their  former  values. 
If,  then,  while  an  electric  force,  E,  exists  between  the  two  plates  of  po- 
tentials V  and  F",  a  dielectric  slab  of  thickness  /  is  introduced  and  at 
the  same  time  the  plates  are  further  separated  by  an  amount  /  —  t/K, 
making  d  +  2t  —  t/K  in  all,  the  surface  density  on  the  plates  and  hence 
the  electric  force,  E,  will  remain  constant.  The  electric  force  is  then 
given  by  the  equation 


V  -  V"  =  E(d  +  2t-  t/k), 
or 

PD  X  io8 
E  ~  d  +  2t  -  t/k1 


(i) 


where  PD  is  the  potential  difference  of  the  two  electrostatic  plates  in 
volts. 

The  cathode  beam  in  passing  through  the  uniform  electric  field,  E, 
is  accelerated  by  a  constant  force  and  hence  follows  Newton's  second 
law.  The  force  on  the  charge  e  will  be 

Ee  =  ma,  (2) 

where  a  is  the  acceleration  toward  the  positive  plate  and  m  is  the  mass  of 
the  electron.  Since  the  electron  falls  through  a  distance  d  in  time  / 
we  have  the  distance  of  fall  expressed  by  the  equation 


d  = 
or 

2d 

°=7-  (3) 

If  the  velocity  in  the  horizontal  direction  is  v  and  the  length  of  horizontal 
travel  is  /  we  have 

/  =  vt, 
whence 

i  ^ 
t*      I2' 

Substituting  this  value  in  equation  (3)  gives 


If  this  value  is  placed  in  equation  (2)  we  have 


320 


L.  T.  JONES. 


[SECOND 

[SERIES. 


whence 


(4) 


If  at  the  same  time  the  moving  electron  is  subjected  to  the  action  of  a 
uniform  magnetic  field  of  intensity  H  and  its  velocity  v  is  perpendicular 
to  the  lines  of  magnetic  force,  urging  the  particle  in  the  path  of  a  circle, 
in  the  plane  of  the  photographic  plate,  then  the  force  is  given  by 


mv* 
Hev  =  — 


(5) 


where  r  is  the  radius  of  the  circle.  If  the  dotted  line,  Fig.  3,  indicates 
the  path  of  the  particle  undeflected  by  the  magnetic 
field,  and  the  circle  of  radius  r  the  curvature  exper- 
ienced under  the  influence  of  the  magnetic  field  of 
strength  H  we  may  represent  the  horizontal  distance 
traveled  by  the  length  /  and  the  magnetic  deflection 
(measured  at  right  angles  to  the  undeflected  path)  by 
2,  since  z  is  small  compared  with  /.  Then,  from 
Fig.  3, 


2r 


and 


Fig.  3. 


since  z2,  being  small  in  comparison  with  I2,  may  be  neglected.     Placing 
this  value  of  i/r  in  equation  (5)  we  have 

e         i         22 
mv  =  Hr~ HI2' 

Elimination  of  e/m  between  (4)  and  (6)  gives 

zE 


(6) 


V  = 


Hd' 


Replacing  E  by  its  value  given  in  (i)  we  get,  after  simplification, 

zPD  X  io8 


~ 


Hd(d  +  2t-  t/K)  ' 
Again,  multiplying  equations  (6)  and  (7)  gives 
e          z2PD  X  2  X  io8 


m  ~  H2J2d(d 


-  t/K)  ' 


(7) 


(8) 


THE  ELECTROSTATIC  FIELD. 

The  two  electrostatic  plates  were  rectangular  brass  plates  7.5X15X1 
cm.     Considerable  difficulty  was  experienced  in  getting  the  two  plates 


No's!"']  METHOD  OF  MEASURING  e/m  AND  v.  321 

sufficiently  plane.  The  plates  were  first  planed  and  then  finished  by 
"spotting"  on  a  master  plate.  A  slip  of  soft  iron  5  X  1.5  X  .15  cm. 
was  inlaid  in  the  upper  plate,  as  shown  in  Fig.  2,  and  the  plate  again 
surfaced.  Several  days  were  required  to  surface  the  plates  but  they  were 
finally  finished  sufficiently  plane  that  one  would  raise  the  other  from  the 
table. 

A  second  slip  of  soft  iron  was  cut  out  5  X  1.5  X  .1  cm.  and  one  side 
made  plane.  A  scratch  .005  cm.  in  width  and  of  about  the  same  depth 
was  drawn  full  length  on  this  surfaced  side.  This  scratch  formed  the 
tube  through  which  the  cathode  rays  passed.  The  iron  slip  with  the 
scratch  was  held  against  the  iron  slip  inlaid  in  the  upper  electrostatic 
plate  by  ten  brass  screws.  On  account  of  the  small  diameter  of  the  scratch 
and  its  relatively  large  length  it  was  subsequently  found  to  be  easier 
to  make  a  scratch  of  about  .05  cm.  in  diameter,  close  each  end  with  a 
small  bit  of  solder,  cut  off  the  solder  flush  with  the  iron  surface  and  then 
make  a  small  scratch  in  the  bit  of  solder  at  each  end.  A  scratch  .1  cm. 
long  at  each  end  was  found  to  give  perfect  satisfaction,  and  not  nearly 
so  much  difficulty  was  experienced  in  getting  the  beam  to  pass  through 
this  tube.  In  adjusting  the  cathode  to  send  a  beam  through  the  tube 
the  electrostatic  plates  were  first  mounted  in  position  with  the  scratch 
the  full  .05  cm.  diameter.  The  vessel  was  exhausted  and  a  potential 
difference  of  about  20  volts  applied  to  the  electrostatic  plates.  The  wax 
joint  where  the  glass  tube  supporting  the  cathode  entered  the  plate  glass 
end  was  then  softened  by  heating  and  the  cathode  moved  about  until  a 
phosphorescent  spot  on  the  willemite  screen,  deposited  on  the  opposite 
glass  end  plate,  showed  the  presence  of  the  beam.  The  wax  was  allowed 
to  cool  while  the  cathode  was  in  the  position  giving  this  spot  its  maximum 
brightness.  The  electrostatic  plates  were  then  removed  by  taking  out 
the  screws  holding  the  ebonite  disc,  B,  to  the  brass  ring,  D,  and  the  tube 
made  smaller  by  the  bits  of  solder  mentioned  above.  The  plates  were 
then  replaced  in  position  and  the  vessel  exhausted.  If  the  spot  failed 
to  show  on  the  willemite  screen  the  process  was  repeated  until  finally 
the  beam  was  made  to  pass  through  the  small  tube. 

An  iron  tube,  /,  .5  cm.  diameter  and  2  cm.  long,  was  screwed  into  the 
disc,  B,  to  shield  the  rays  from  any  magnetic  effect  before  entering  the 
confining  tube.  The  cathode  was  within  I  cm.  of  the  tube  I. 

The  electrostatic  plates  were  spaced  by  four  hollow  ebonite  cylinders, 
one  placed  at  each  corner,  and  clamped  in  position  by  ebonite  bolts 
passing  through  the  cylinders.  The  length  of  these  cylinders  was 
measured  by  a  micrometer  caliper  reading  to  .001  cm.  The  cylinder 
was  placed  between  two  thin  glass  plates  and  the  length  of  the  whole 


322  L.  T.  JONES. 

measured.  The  thickness  of  the  plates  was  then  subtracted.  Each 
cylinder  was  measured  on  several  successive  days  and  the  mean  of  these 
measurements  was  taken  as  the  length.  When  the  cylinders  were  again 
measured,  after  having  been  in  the  apparatus  under  pressure  for  four 
months,  they  were  found  to  have  shortened  by  about  I  per  cent.  All 
data  was  taken  during  the  first  fifteen  days,  however,  so  no  correction 
was  made  for  this  change  in  length.  The  potential  difference  of  the 
electrostatic  plates  was  determined  as  follows:  A  high  potential  storage 
battery,  7s,  was  used  in  sending  a  small  current  through  the  two  high 
resistances,  M  and  R,  as  shown  in  Fig.  4.  M  was  a  resistance  of  about 
2  X  io6  ohms  while  R  was  an  adjustable  resistance  of  about  10,000  ohms. 
The  electrostatic  plates  were  connected  directly  to  the  terminals  of  M 
as  shown.  By  adjusting  the  value  of  R  the  potential  difference  of  the 
terminals  of  M  could  be  kept  constant.  The  potential  drop  through  a 

small  part  of  M  was  meas- 
ured by  a  potentiometer, 
P,  against  a  Weston  stand- 
ard cell  of  1.0185  volts  at 
24°  C.  The  potential  dif- 
ference of  the  electrostatic 
Fig.  4. 

plates  was  thus  easily  meas- 
ured to  .1  per  cent,  and  by  means  of  R  the  value  was  kept  constant  to 
within  .1  volt. 

THE  MAGNETIC  FIELD. 

The  magnetic  field  was  furnished  by  a  solenoid  of  648  turns  and 
160.2  cm.  length.  The  solenoid  was  built  in  two  parts  and  made  to  join 
closely  at  the  middle  so  as  to  enclose  the  whole  tube.  The  length  of  the 
solenoid  was  such  that  the  field  could  be  considered  uniform  and  calcu- 
lated. From  the  dimensions  of  the  solenoid  the  strength  of  the 
magnetic  field  at  its  center  was  given  by 

H  =  5.083  7, 

where  /  is  the  strength  of  the  current  in  amperes.  The  current  for  the 
magnetic  field  was  supplied  by  storage  cells  of  40  amperes  capacity. 
The  current,  which  varied  between  .5  and  1.5  amperes,  was  measured 
by  a  Siemens  &  Halske  ammeter  reading  to  .005  amperes. 

RESULTS. 

In  placing  the  photographic  plate  in  the  apparatus  for  exposure  the 
plate  was  placed  solidly  against  the  ebonite  disc,  B.  The  iron  confining 
tube  for  the  cathode  beam  was  5.08  cm.  long  and  hence  a  line  drawn 


PHYSICAL  REVIEW,  VOL.  III..  SECOND  SERIES. 
May,  1914. 


PLATE  I. 
To  face  page  322. 


No.  18. 


No.  3. 
Fig.  5. 

L.  T.  JONES. 


VOL.  III.] 
No.  5. 


METHOD  OF  MEASURING  e/m  AND  v. 


323 


across  the  plate  5.08  cm.  from  the  end  that  touched  the  ebonite  disc 
established  the  zero.  This  line,  marked  0  in  the  photographs,  was  then 
directly  under  the  opening  of  the  tube.  The  length  of  horizontal  travel, 
/,  was  measured  from  this  line.  In  photograph  6  two  calculations  of 
e/m  were  made,  where  the  distance  /  was  4  and  5  cm.  respectively.  In 
each  photograph  the  long  streamer,  second  from  the  top,  is  the  central 
one,  given  by  zero  magnetic  field.  The  two  spots  immediately  on  either 
side  are  for  the  magnetic  deflection,  direct  and  reversed.  The  additional 
spots  seen  have  no  significance  relative  to  the  value  of  e/m.  The  magnetic 
deflections  were  accurately  measured  along  the  lines  drawn  parallel  to 
the  line  marked  0.  The  reproductions  in  Fig.  5  are  full  size.  Twenty 
photographs  were  taken  in  succession.  Table  I.  gives  the  data  relative 
to  all  these. 

TABLE  I. 


Plate  No. 

7 

PD. 

z. 

i 

d. 

t. 

d+2t_t 

•V  X  10-9. 

—  XIO-7. 

^ 

MM 

1 

.460 

524.0 

.138 

4.0 

.835 

.165 

.292 

2.866 

2.114 

2 

.450 

564.4 

.127 

4.0 

.820 

.180 

.210 

3.158 

2.192 

3 

.890 

498.1 

.245 

4.0 

.825 

.175 

.204 

2.715 

1.838 

4 

.8902 

639.7 

.220 

4.0 

.830 

.160 

.177 

3.183 

1.935 

6 

.885 

425.0 

.251 

4.0 

.811 

.179 

.199 

2.438 

1.701 

6a 

.885 

425.0 

.3116 

5.0 

.811 

.179 

.199 

3.027 

1.678 

7a 

.850 

323.5 

.325 

5.0 

.805 

.185 

.206 

2.506 

1.508 

7b 

.850 

323.5 

.371 

5.5 

.805 

.185 

.206 

2.861 

1.624 

Ic 

.850 

323.5 

.397 

6.0 

.805 

.185 

.206 

3.061 

.563 

Sa 

.8725 

323.0 

.314 

4.5 

.805 

.185 

,206 

2.355 

.647 

86 

.8725 

323.0 

.372 

5.5 

.805 

.185 

.206 

2.790 

.547 

9 

.879 

320.3 

.335 

5.0 

.810 

.180 

.200 

2.470 

.482 

Wa 

.864 

301.0 

.389 

5.0 

.825 

.165 

1.182 

2.734 

.937 

106 

.864 

301.0 

.423 

6.0 

.825 

.165 

1.182 

2.973 

.591 

11 

.867 

299.0 

.377 

5.0 

.826 

.164 

1.181 

2.622 

.807 

12a 

.873 

298.0 

.405 

5.0 

.826 

.164 

.181 

2.788 

.036 

126 

.873 

298.0 

.461 

6.0 

.826 

.164 

.181 

3.173 

.832 

13 

.872 

298.0 

.382 

5.0 

.824 

.166 

.184 

2.632 

.815 

14a 

.874 

284.2 

.4335 

5.5 

.819 

.171 

.189 

2.947 

.837 

146 

.874 

284.2 

.499 

6.5 

.819 

.171 

.189 

3.278 

1.735 

15 

.881 

247.2 

.467 

6.0 

.817 

.173 

.192 

2.647 

1.533 

17 

.450 

248.6 

18 

.453 

246.6 

19 

.4515 

245.3 

20 

1.289 

296.7 

.558 

5.3 

.850 

.140 

1.153 

2.578 

1.563 

Average 

1.748 

The  value  of  the  dielectric  constant  of  the  glass  plate  was  that  given 
by  Landolt  and  Bornstein  for  "  spiegel  glas."  If  the  value  of  K  was  taken 
as  either  5  or  7  instead  of  6  the  resulting  value  of  e/m  is  changed  by  only 


324  L'  T'  JONES' 

about  .5  per  cent.     The  probable  error  of  the  final  result,  calculated  in 
the  usual  way  from  the  data  in  Table  I.,  is  1.5  per  cent. 

SUMMARY 

The  method  devised  for  the  determination  of  e/m  and  v  for  cathode 
rays  from  a  cold  cathode  is  a  modification  of  the  usual  electrostatic  and 
magnetic  deflection  photographic  method.  It  has  two  distinct  ad- 
vantages. 

1.  Both  the  electrostatic  and  magnetic  fields  are  uniform  over  the 
entire  path  of  the  deflected  cathode  beam. 

2.  The  electrostatic  deflection  is  kept  constant  for  all  strengths  of 
fields  employed  and  thus  the  inaccuracy  in  its  measurement  is  eliminated. 

The  mean  of  twenty  successive  photographs  gave 

e/m  =  1.75  .=*=  .03  X  io7. 

I  wish  to  express  my  appreciation  to  Dr.  C.  T.  Knipp  for  his  kindly 
suggestions  and  to  Professor  A.  P.  Carman,  Director  of  the  Laboratory, 
for  the  facilities  offered. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
January  20,  1914. 


Reprinted  from  School  Science  and  Mathematics,  Vol.  14,  1914. 

Pages  555-562. 


THE  DETERMINATION  OF  E/M  FOR  CATHODE  RAYS  AS  A 

LABORATORY    EXPERIMENT    FOR   AN    UNDERGRADUATE 

COURSE  IN  ELECTRICAL  MEASUREMENTS. 

BY  CHAS.  T.  KNIPP, 
University  of  Illinois,  Urbana. 

The  numerical  value  of  the  ratio  of  the  charge  to  the  mass  of 
the  cathode  ray  particle  or  electron  is  no  longer  a  problem  for  the 
research  laboratory.  It  is  as  truly  a  constant  as  is  the  heat  of 
fusion  of  ice,  or  Joule's  mechanical  equivalent,  and  its  value  is 
nearly  as  accurately  knov.n.  However,  its  experimental  deter- 
mination is  generally  considered  to  be  fraught  with  manipulative 
difficulties  of  considerable  moment,  which  under  the  ordinary 
conditions  of  laboratory  equipment  makes  it  an  extremely  difficult, 
if  not  an  impossible,  experiment  for  undergraduates. 

The  recent  development  of  the  electron  theory  with  its  bearing 
upon  the  nature  of  electricity  and  the  probable  constitution  of 
matter  is  so  fundamental  and  far-reaching  that  it  seems  quite 
proper  that  one  or  more  of  these  comparatively  new  and  yet 
apparently  more  difficult  experiments  should  be  included  in  an 
undergraduate  course  in  electrical  measurements.  Hence  the  fol- 
lowing elementary  theory  for  the  determination  of  e/m  for  cath- 
ode rays  is  presented  as  an  instructive  and  practical  experiment. 
For  pedagogical  reasons  the  discussion  is  given  as  recently  pre- 
sented to  a  class  in  electrical  measurements  for  juniors.  The 
apparatus  necessary  consists  of  a  Braun  tube  having  a  pair  of 
electrostatic  field  plates  inside,  a  three-inch  induction  coil,  and 
a  high  potential  battery  capable  of  furnishing  potential  differences 
up  to  500  volts,  also  a  commutator,  a  simple  water  resistance  and 
a  voltmeter. 

The  more  important  characteristic  properties  of  the  cathode 
rays  are — they  travel  in  straight  lines  and  have  a  high  velocity, 
the  electrons  composing  the  rays  each  carry  a  negative  elementary 
charge,  they  are  deflected  by  either  a  magnetic  or  an  electrostatic 
field,  they  apparently  have  a  mass  that  is  1/1700  that  of  the 
hydrogen  atom,  they  may  ionize  a  gas  through  which  they  pass. 


550 


SCHOOL  SCIENCE  AND  MATHEMATICS 


and  upon  striking  an  object  they  cause  that  object  to  emit  Roent- 
gen rays. 

The  charge  on  the  electron  and  the  mass  of  the  electron  are 
severally  quite  difficult  to  determine.  However,  their  ratio, 
e/m,  is  comparatively  easy  of  measurement.  The  velocity  of  the 
electron  also  admits  of  easy  measurement.  In  the  theory  that  fol- 
lows, the  property  of  the  magnetic  and  electrostatic  deflection  of 
these  rays  is  employed. 

(a.)     ELECTROSTATIC  DEFLECTION  OF  A  MOVING  ELECTRON/ 


-o^  — -^  B 

FIGURE  1. 
In  Figure  1  let 

OX  =  path  of  undeflected  beam. 
MN  =  electrostatic  field  plates. 
AB  =  screen. 

Y  =  electric  force  per  cm.  between  plates. 
d  =  length  of  field  plates. 

/  =   distance  of  screen  from  opening  O  in  diaphragm. 
y  =  electrostatic  deflection  on  screen. 

Let  the  lower  plate  be  charged  positively  and  the  upper  one 
negatively,  and  suppose  that  the  field  ends  abruptly  at  the  edge 
of  the  plates  (the  error  is  quite  negligible  if  the  plates  are  close 
together).  The  electron  in  moving  through  the  uniform  electric 
field  is  urged  toward  the  positive  plate  with  a  force  Y^  and  its 
equation  of  motion  is 


where  —^  is   its   acceleration   in   the   v-direction.     From   which 

Accel.  =  —  =  a. 

m 

Applying  the  laws  of  falling  bodies,  the  deflection  becomes 
-.lfl/2=    i-     X*     — 


JThomson,   Conduction  of  Electricity   through   Gases,   2d   Ed.,   p.   117. 


DETERMINATION   OF  E/M  FOR  CATHODE  RAYS        55? 

and  the  velocity  downward  is  given  by 

Ye       d 
Vmn^at=,_._ 

The  path  of  the  electron  from  the  edge  of  the  field  plates  to  the 
screen  AB  is  a  straight  line,  hence  the  additional  deflection  down- 
ward in  traveling  this  distance  is 

,„       Ye      d      l—d 
y'-VmnXt--  -•-•  —  • 

Therefore  the  whole  distance  downward  is 


1 

Ye 

d2    , 

Y£> 

d 

l—d 

2 

mv- 

m 

*2     ' 

K-' 

\     &  / 

m 

}' 

V 

V 

which  may  be  written, 


—-,-  »  (1) 

mv* 


where  A  is  a  constant  depending  upon  the  geometrical  data  of 
the  discharge  tube.  It  should  be  noted  that  the  electrostatic  de- 
flection is  inversely  proportional  to  the  energy  of  the  moving 
electron. 

(b.)     MAGNETIC  DEFLECTION  OF  A  MOVING  ELECTRON. 

For  convenience  in  discussing  make  the  magnetic  field 
coterminous  with  the  electric  field.  Let  the  shaded  portions  in 
Figure  1  represent  the  pole  pieces.  The  magnetic  lines  are  then 
parallel  to  electric  lines  of  force.  As  in  the  electric  case,  con- 
sider that  the  magnetic  field  ends  abruptly  at  the  edge  of  the 
pole  faces. 

It  was  shown  by  Rowland  and  others  that  a  moving  charged 
particle  is  equivalent  to  a  current  of  electricity,  or 

i  =  ev, 

where  e  is  the  charge  on  the  particle  and  v  its  velocity.  A  con- 
ductor carrying  a  current  in  a  magnetic  field  is  urged  by  a  force  at 
right  angles  to  both  the  direction  of  field  and  current.  The  mag- 
nitude of  this  force  is 

F  =  Hi  =  Hev. 

In  a  uniform  magnetic  field  the  electron,  under  the  action  of  a 
constant  force  at  right  angles  to  its  direction  of  motion,  moves 
in  a  circular  path.  By  a  theorem  in  mechanics  its  normal  accelera- 
tion towards  the  center  is 


558  SCHOOL  SCIENCE  AND  MATHEMATICS 

a'  -  ^  , 

P 

where  p  is  the  radius  of  the  circle;  and  the  force  towards  the 
center  is  equal  to 


massXaccel.  = 

p 

Hence  the  equation  of  motion  for  a  moving  electron  in  a  uniform 
magnetic  field  is 


or 

1      _  He 

p  lill' 

This  force  urges  the  electron  in  the  ^-direction,  i.  e.,  in  a  direction 
perpendicular  to  the  plane  of  the  paper.  To  evaluate  1/p  con- 
struct a  circle  of  diameter  2p  and  lay  off  d,  the  length  of  pole 
face,  and  smn,  the  magnetic  deflection,  as  shown  in  Figure  2. 
Draw  the  additional  lines  indicated.  Then,  from  the  similar  right 
angled  triangles,  it  follows  that 


FIGURE  2. 


2p 


from  which 


d2 


=  —  approximately, 


since  smn  is  small  in  comparison  with  d.  Therefore 

He 


mv 


Following  the  same  line  of  development  as  in  the  electrostatic 
case,  the  velocity  at  m,  in  the  ^-direction  is  given  by 


DETERMINATION   OF  E/M  FOR  CATHODE  RAYS        559 

-        d        Hed 


m 


The  additional  magnetic  deflection  is 


m          ? 
Hence  the  total  manetic  deflection  becomes 


fm'JL    M^    ^,H^    l~d 

2      mv  m          v 


mv 
which  may  be  written 

"R  '  Y9\ 

3  =  D     •    -     ~    •  { ~ ) 

where  B,  as  in  the  electric  case,  is  a  constant  depending  upon  the 
geometrical  data  of  the  discharge  tube.  The  magnetic  deflection  is 
inversely  proportional  to  the  momentum  of  the  moving  electron. 
It  should  be  remarked  that  both  equations  (1)  and  (2)  are  true 
for  heavy  carriers  (atomic  or  molecular)  having  either  positive  or 
negative  charges. 

For  coterminous  fields 

A  =  B. 

By  applying  the  two  fields  simultaneously  and  at  the  same  time 
giving  them  the  proper  directions  the  spot  on  the  screen  will  take 
up  its  position  at  some  point  P,  whose  co-ordinates  are  3-,  z. 
Obviously,  under  these  conditions,  either  the  velocity  v,  or  the 
ratio  e/m  may  be  calculated  by  combining  the  two  equations. 
Eliminating  v  between  (1)  and  (2)  gives 

AY<?      J^        EHe      _1_ 
mv         y  m          z 

from  which 

AY       * 
BH~  '  ~y~ 

Substituting  this  value  of  v  in  (2)  and  solving  gives  for  the 
ratio  of  the  charge  to  the  mass, 

P  A  V  «.2 

e      =      A  *         .    ^_  (A\ 

m  ~     B2H2       y 

APPLICATION  TO  THE  BRAUN  TUBE. 

This  experiment  may  be  performed  in  the  case  of  the  Braun 
tube,  by  using  the  intensity  of  the  earth's  magnetism  in  place  of 


560  SCHOOL  SCIENCE  AND  MATHEMATICS 

the  usual  solenoid  or  electromagnet.  The  relative  position,  for 
the  particular  tube  used,  of  the  aperature  O,  the  electric  field 
plates  MN,  and  the  screen  AB  is  shown  in  Figure  3.  From  the 
dimensions  given 

A  -  rf  (/-  -|-)  ==  8  (32-  A)  _  2.24X10=, 
and 

vxio8 


Y 


2.4 


M         - 


-r^2.4cm. 


4 -8cm — >     V 

4.  _ \32cm. > 

4 —33  cm.  - » 

FIGURE  3. 

where  V  is  the  potential  difference  in  volts  between  the  plates 
M  and  N. 

Again,  the  constant  B  becomes,  since  the  magnetic  field  acts 
over  the  entire  distance  OX  and  hence  d  =  l, 
I2         332 


and 


Equations  (3)  and  (4)  thus  become,  for  this  particular  tube, 


and 

e  \i  v2 

i-^iP-f-104  (^ 

where  H,  as  suggested  above,  is  the  magnetic  field  due  to  the 
earth. 

Now  for  H  either  the  total  intensity  or  the  horizontal  com- 
ponent may  be  used.  The  former  gives  the  larger  deflection,  how- 
ever the  difficulty  of  inclining  the  tube  at  the  proper  angle  is 
considerable,  especially  within  a  building  having  an  iron  frame- 
work, hence  it  is  more  reliable  and  the  experiment  easier  to  per- 
form when  using  the  horizontal  component.  The  vertical  com- 
ponent, while  it  displaces  the  spot  on  the  screen  to  the  north  or 


DETERMINATION  OF  E/M  FOR  CATHODE  RAYS        561 

south  (depending  on  the  orientation  of  the  tube),  introduces  no 
error  since  the  direction  of  the  electrostatic  field  is  reversed  in 
taking  readings  for  each  position  of  the  tube.  To  enable  the  tube 
to  be  placed  in  these  various  positions  quickly  and  accurately  it 
should  be  mounted  on  a  wooden  frame  that  will  admit  of  rota- 
tion of  the  tube  about  a  vertical  and  also  a  horizontal  axis,  as 
shown  in  Figure  4.  The  value  of  H  (the  horizontal  component) 
at  the  point  in  the  laboratory  where  the  experiment  was  per- 
formed was  previously  determined  by  comparison  with  the  value 
of  H  out  in  the  open  and  about  one  mile  from  local  magnetic 
disturbances,  and  was  found  to  be 

H  =  .160 


FIGURE  4. 

Typical  sets  of  data  are  contained  in  Tables  I  and  II.  The  con- 
ditions that  obtained  in  the  two  sets  were  the  same  with  one  im- 
portant exception.  In  Table  II  the  precaution  was  taken  to  shield 
that  portion  of  the  Braun  tube  between  the  cathode  and  the  dia- 
phragm O  from  the  earth's  magnetic  field  by  wrapping  it  with  two 
layers  of  annealed  sheet  iron.  This  shield  was  connected  to  earth. 
The  effect  of  the  shielding  was  quite  noticeable  in  that  the  spot  on 
the  screen  was  brighter  and  steadier,  thus  enabling  the  deflections 


562 


SCHOOL  SCIENCE  AND  MATHEMATICS 


to  be  more  accurately  read.  The  values  of  v  are  considerable  in 
excess  of  those  obtained  by  more  refined  apparatus,  while  the 
values  of  c/m  agree  indeed  very  closely  with  the  generally  ac- 
cepted value  which  is  1.77X107-  In  fact  the  apparatus  scarcely 
warrants  such  close  agreement,  yet  repeated  observations  with 
widely  different  voltages  gave  values  for  c/m  in  excess  but  a  few 
per  cent  of  the  true  value. 

TABLE   I. 


Readings   on    Screen   A  13. 
Bulb  to  West     II         Bulb  to  East 
Direct  (Reversed  ||      Direct     [Reversed 

Mean 
Mag. 
defl. 
in    cm. 

Mean 
Electric 
defl. 
in    cm. 

V*  in 
Volts 

t/xio-o 

e/mXIO-' 

Z 

48 
47 
47 

Y 

•24 
17 
14 

Z 

48 
47 
47 

Y 
33 

38 
43 

Z 

51 
51 

5  12 

Y 

24 
17 
82 

Z 

51 
51 
51 

Y 

34 
38 
43 

.13 

.2 
.2 

y 

.475 
1.05 
1.60 

190 
372 
542 

6.4 

7.5 
7.2 

1.10 
1.74 
1.66 

Average,  1.50 

TABLE   II. 

42 
42.5 
42 

27 

20 
14 

42 
42.5 
43 

37.5 
42 
47.5 

|46 
146.5 

|47 

27.5 
19 
13 

46 
47.5 

482 

38 
42 
47.5 

.2 
.225 
.25 

.525 
1.125 

1.70 

206 
409 
625 

8.4 

8.7 
9.8 

1.93 
1.78 
1.84 

Average,    1.85 

In  conclusion  it  is  but  fair  to  mention  that  the  preliminary  work 
of  testing  out  this  experiment  was  ably  done  by  F.  E.  Faulkner 
and  E.  A.  Reid,  seniors  in  the  University.  It  was  presented  later 
as  a  regular  experiment  (on  trial)  before  three  sections  of  juniors 
in  electrical  engineeering  as  an  experiment  in  electrical  measure- 
ments. The  accuracy  of  the  results  and  the  favor  with  which  the 
experiment  was  received  seem  to  warrant  the  purchase 'of  addi- 
tional tubes  and  making  it  a  regular  experiment  to  be  performed 
by  under-graduates  taking  a  course  in  exact  electrical  measure- 
ments. 

2  Unsteady. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  Ill,  No.  6,  June,  1914.] 


AN    ATTEMPT   AT   AN    ELECTROMAGNETIC    EMISSION 
THEORY  OF  LIGHT. 

BY  JAKOB  KUNZ. 

THE  principle  of  relativity  gives  a  consistent  explanation  of  the 
phenomena  of  aberration  of  light,  of  the  experiments  of  Fizeau 
and  Michelson-Morley,  and  of  the  increasing  mass  of  the  electron  as 
function  of  the  velocity.  The  new  principle  rejects  the  ether,  in  which 
according  to  the  older  theory  light  waves  are  propagated  and  in  which 
the  electric  and  the  magnetic  energies  have  their  seat.  We  are  concerned 
again  with  actions  at  a  distance,  without  a  medium,  but  with  actions 
proceeding  with  the  velocity  of  light. 

The  mathematical  simplicity  of  the  original  principle  of  relativity 
was  mainly  due  to  the  fact  that  it  used  a  fundamental  constant,  the 
velocity  of  light  c  as  an  absolute  constant,  so  that  the  Lorentz  trans- 
formation can  be  applied  to  Maxwell's  equations,  which  remain  un- 
changed. 

Recently  A.  Einstein1  generalized  the  original  principle  and  applying 
it  to  the  field  of  gravity  came  to  the  conclusion  that  c  must  not  be  con- 
sidered as  a  constant  but  as  a  function  of  the  coordinates.  If  the  con- 
clusion of  this  investigation  is  confirmed  by  the  experiment,  then  the 
original  theory  of  relativity  fails  and  if  it  is  not  confirmed,  the  theory 
of  relativity  will  be  beset  with  great  difficulties.  In  either  case  it  will 
only  be  an  approximation  to  the  physical  reality. 

If  we  consider  the  material  bodies  as  completely  separated  but  exerting 
forces  on  each  other,  then  the  action  at  a  distance  remains  incompre- 
hensible at  all  events;  but  if  there  is  no  medium,  we  should  expect  in 
accordance  with  the  Newtonian  theory  of  gravity  an  action  at  a  distance 
with  infinite  velocity,  and  as  a  matter  of  fact  we  do  not  know  whether 
gravity  proceeds  with  finite  or  infinite  velocity.  If  however  in  the 
theories  of  relativity  it  is  assumed  that  the  action  proceeds  with  constant 
or  variable  finite  velocity,  then  the  phenomena  become  even  more  mys- 
terious. 

The  principle  of  relativity,  even  in  its  simple  original  form,  affects  our 

1  A.  Einstein,  "Entwurf  einer  verallgemeinerten  Relativitatstheorie,"  Zeitschrift  fur 
Mathematik  und  Physik,  Band  62,  p.  225,  1914. 


465  JAKOB  KUNZ. 

notions  of  space  and  time.  Time,  once  absolute,  dwindles  to  a  mere 
shadow.  The  simultaneity  of  two  events  and  the  equality  of  two  time 
intervals  become  relative,  the  parallelogram  of  velocities  appears  only 
as  an  approximation,  an  absolutely  solid  body  is  impossible  and  the  mass 
of  a  body  depends  on  its  velocity. 

When  a  physical  theory  which  is  mathematically  complicated  and  is 
only  an  approximation  cuts  so  deeply  in  our  fundamental  notions,  and 
renders  the  phenomena  so  incomprehensible,  the  freedom  of  advancing 
other  theories,  which,  though  more  conservative,  attempt  to  coordinate 
the  various  phenomena  in  question  should  be  granted.  In  the  following 
a  theory  will  be  .developed  which  agrees  with  that  of  relativity  in  many 
features,  but  gives  an  entirely  different  aspect  of  the  world. 

§  i.   FUNDAMENTAL  ASSUMPTIONS. 

1.  One  of  the  theories  other  than  that  of  relativity  is  the  electro- 
magnetic emission  theory  of  light.     It  is  a  compromise  between  the  emis- 
sion theory  and  the  wave  theory.     Each  electric  charge  is  supposed  to 
be  surrounded  by  an  electromagnetic  field  residing  in  the  medium,  which 
field  itself  forms  the  mass  of  the  charge.     Thus  instead  of  having  a  con- 
tinuous medium,  ether,  we  have  as  many  media  as  there  are  electric 
charges.     Each  individual  electromagnetic  field  extends  throughout  the 
universe,  but  is  essentially  concentrated  in  the  immediate  neighborhood 
of  the  electron.     No  assumption  is  made  as   to  the  structure  of  the 
elementary  medium. 

2.  Maxwell's  equations  will  be  applied  to  the  molecular  fields.     The 
expressions  for  the  masses  of  fields  at  rest  will  be  extended  to  fields  in 
motion. 

3.  The  velocity  of  light  is  always  equal  to  c  for  a  vacuum.     While  in 
a  mechanical  emission  theory  the  velocity  v  of  the  source  is  added 
geometrically  to  the  velocity  c,  we  have  in  the  present  theory,  through 
a  process  of  compensation,  the  velocity  of  light  always  equal  to  c,  and 
independent  of  the  velocity  of  the  source.     The  difference  between  a 
mechanical  emission  theory,   the  undulatory  theory  and    the  electro- 
magnetic emission  theory  of  light  can  be  illustrated  by  the  following 
figures. 

The  source  of  light  moves  with  the  velocity  v  per  second  from  A  to  B 
towards  the  observer.  In  the  mechanical  emission  theory  the  light  par- 
ticles emitted  in  the  point  A  with  the  velocity  c  would  lie  after  a  second 
on  the  sphere  with  radius  c  and  with  the  center  B.  Thus  the  center  of 
the  wave  front  would  always  coincide  with  the  source  itself.  In  the 
undulatory  theory,  where  the  light  is  carried  through  the  continuous 


VOL.  Ill  I 
No.  6.     . 


THEORY  OF  LIGHT. 


466 


independent  medium,  the  center  of  the  disturbance  would  always  co- 
incide with  the  point  A  in  which  it  has  been  emitted.  In  the  electro- 
magnetic emission  theory  the  center  of  the  disturbance  would  coincide 
with  the  moving  source  but  the  wave  surface  would  be  an  ellipsoid  of 
revolution  whose  equatorial  plane  is  perpendicular  to  the  direction  of 


Fig.  1. 


Fig.  2. 


Fig.  3. 


motion.  In  the  second  and  third  cases  the  velocity  of  light  is  always 
equal  to  c.  In  the  second  case  the  motion  of  the  material  luminous 
source  has  an  influence  on  the  optical  phenomena,  so  we  could  hope  to 
discover  the  motion  of  the  source  with  respect  to  the  ether  and  if  the 
ether  were  at  rest  we  could  hope  to  discover  the  absolute  motion  of  the 
source.  This  is  impossible  by  mechanical  methods  according  to  New- 


\  \t 


Fig.  4. 


Fig.  5. 


ton's  principle  of  relativity.  In  the  first  and  third  theory  we  could 
not  discover  the  absolute  motion  of  the  source.  The  critical  velocity 
c  of  light  in  the  vacuum  is  in  Maxwell's  theory  equal  to  the  ratio 
of  the  electrostatic  to  the  electromagnetic  unit  of  electric  charge.  If 
we  consider  c  as  constant  and  maintain  Maxwell's  equations  unchanged 
for  an  electromagnetic  field  in  motion,  we  consider  that  ratio  of  the 
two  units  also  as  independent  of  the  motion.  This  means  that  the 
ratio  of  the  force  which  on  the  one  hand  unit  charge  exerts  upon 
another  charge  in  a  given  distance  to  the  force  which  on  the  other 
hand  the  same  unit  charge,  when  in  motion  exerts  upon  a  magnet  is 
independent  of  a  uniform  motion  of  the  whole  system.  It  is  sufficient, 
but  not  necessary,  for  this  purpose  to  assume  that  an  electric  charge 


467  JAKOB  KUNZ. 

exerts  upon  another  charge  the  same  force,  no  matter  whether  both  are 
at  rest  or  in  uniform  motion ;  further,  that  an  electric  current  exerts  the 
same  influence  upon  a  magnet  independent  of  the  state  of  rest  or  of  uni- 
form motion  of  the  whole  system.  In  this  way  may  be  explained  the 
facts  that  the  electrostatic  field  of  the  earth,  revolving  round  the  sun, 
produces  no  magnetic  effects,  and  the  magnetic  field  of  the  earth  no 
electric  effects  by  electromagnetic  induction  upon  bodies  which  are 
rigidly  connected  with  the  earth. 

4.  As  there  is  no  independent  medium  like  ether,  we  are  only  con- 
cerned with  relative  motions  between  charges,  magnets,  sources  of  light 
and  observers.  An  absolute  motion  of  an  electromagnetic  system  with 
constant  velocity  in  a  straight  line  can  not  be  defined  nor  measured  with 
optical  and  electrical  methods. 

The  third  and  fourth  assumptions  lead  to  the  Lorentz  transformation 
of  Maxwell's  equations.  There  is  however  another  transformation 
carried  out  by  Maxwell  and  Hertz  who  found  that  the  essential  form  of 
the  equations  remains  unchanged  if  they  are  related  to  a  system  of  axes 
at  rest  with  respect  to  the  ether  or  in  motion  similar  to  that  of  a  rigid 
body;  in  other  words,  the  absolute  translation  or  rotation  of  a  rigid 
system  of  bodies  has  no  influence  upon  its  internal  electromagnetic 
phenomena,  provided  that  all  bodies  of  the  system,  the  atomic  fields 
included,  take  part  in  the  motion.  The  electric  and  magnetic  fields 
seem  to  be  rigidly  connected  with  the  material  bodies.  The  laws  of 
geometrical  optics  are  therefore  independent  of  the  motion  of  the  earth. 

The  question  still  arises  why  according  to  this  theory  we  can  only 
discover  relative  motions  between  charges  or  magnets  and  between  light 
sources  and  observers.  In  the  first  examples  of  course  the  reason  lies  in 
the  interaction  of  the  fields,  but  why  should  the  field  around  a  source  of 
light  contract  in  the  equatorial  plane  if  it  approaches  an  observer?  The 
reason  may  lie  in  the  pressure  which  the  light  exerts  upon  the  observer 
and  which  the  observer  exerts  on  the  source.  It  might  finally  be  possible 
that  all  the  fields  with  which  we  can  carry  our  experiments  are  imbedded 
as  it  were  in  a  universal  field  of  force. 

§  2.  THE  MASS  OF  THE  ELECTRON. 

An  electron  moves  slowly  in  a  medium  whose  permeability  and  dielec- 
tric constant  are  equal  to  unity.  It  is  accompanied  by  a  material  electric 
field  which,  for  small  velocities,  is  symmetrical  round  about  the  spherical 
electron  so  that  in  a  distance  v  from  the  center  the  electric  force  E  is 
equal  to  E  =  e/r2  and  the  magnetic  force  is  equal  to  H  =  ev  sin  &/r2  = 
Ev  sin  #;  the  magnetic  energy  per  unit  volume  is  equal  to 


THEORY  OF  LIGHT.  468 


2 


sn 


is  the  mass  per  unit  volume. 

sin 


or  for  fj,  =  i 

E2  sin2  tf 

Wi  =  - 
47T 

ing*'     a' 


47T 

/z  is  the  permeability  and  k  the  dielectric  constant.  For  the  following 
considerations  it  will  be  sufficient  to  put  ju  and  k  equal  to  I.  The  mass 
dm  of  an  infinitesimal  ring  will  be  equal  to  : 

e2 
dm  =  —  7  sin2  &  2irr2dr  sin  $  d& 


and  the  whole  mass  will  be  equal  to  : 

2  62 

m  =  --  =  Wo, 

3  « 

where  a  is  the  radius,  e  the  charge  of  the  electron.  This  mass  extends 
for  an  isolated  electron  throughout  the  whole  space,  but  half  of  the  mass 
is  concentrated  in  the  immediate  neighborhood  of  the  electron,  that  is  in 
a  sphere  whose  radius  a\  =  2a. 

If  the  electron  moves  with  finite  velocity,  then  the  electric  field  changes 
in  such  a  way  that  the  lines  of  electric  force  rotate  towards  the  equatorial 
plane,  which  is  perpendicular  to  the  direction  of  motion  v.  At  the  same 
time  the  lines  of  magnetic  force  accumulate  more  and  more  in  that  plane 
as  the  velocity  v  increases.  If  finally  the  critical  velocity  c  is  reached, 
the  whole  electromagnetic  field  will  be  concentrated  in  that  plane  and  the 
mass  of  the  electron  will  increase  indefinitely,  so  that  an  electric  charge 
can  not  move  with  a  velocity  greater  than  that  of  light.  We  see  also 
that  in  this  limiting  case  the  electron  must  cease  to  emit  light  in  the 
direction  of  motion. 

For  a  velocity  v  smaller  than  c  we  have  : 


E 


62(i  -|)  sin2* 
dm  =  -  —  2irr2dr  sin  &  dd, 


469  JAKOB  KUNZ. 

whence 

sin3  #  d$ 
m  =  -( 


The  integrations  are  to  be  extended  over  the  whole  field  outside  the 
electron.  We  do  not  know  the  shape  of  the  electron,  be  it  at  rest  or  in 
motion.  But  there  is  a  tension  in  the  direction  of  electrical  lines  of 
force,  and  hence  a  resultant  tension  acting  on  the  electron,  especially 
round  about  the  equator  and  the  electron  will  assume  the  shape  of  an 
ellipsoid  of  revolution.  According  to  the  law  which  governs  the  equi- 
librium between  internal  and  external  forces,  the  mass  as  function  of  the 
velocity  will  be  different.  The  integration  will  be  carried  out  for  three 
different  conditions  as  follows  : 

I.  The  electron  preserves  the  shape  of  a  sphere  during  the  motion.1 
The  result  of  the  integration  is  this: 


2.  The  form  of  the  electron  changes  according  to  the  law 


a  v2 

b  = 
the  integration  yields  the  result 


m 


the  expression  which  relativity  gives  for  the  transversal  mass  of  the 
electron. 

3.  The  electron  changes  according  to: 


the  integration  gives 


mQ      8v       v2      U2  -  v2      4;  v  i6(c2  - 


The  first  formula  gives  results  which  are  smaller  by  I  ...  3  per  cent. 
than  the  experimental  values  of  C.  E.  Guye  and  S.  Ratnowsky,  which  are 
however  a  little  larger  than  those  calculated  by  means  of  Abraham's 

1  J.  Kunz,  "Determination  theorique  de  la  variation  de  la  masse  de  1'electron  en  fonction 
de  la  vitesse,"  Archives  des  sciences  physiques  et  naturelles  de  Geneve,  1913- 


Na  e"1*]  THEORY  OF  LIGHT.  47O 

formula.  The  third  formula  gives  values  too  large  and  increasing  too 
rapidly,  while  the  second  formula  corresponding  to  relativity  is  in  best 
agreement  with  the  facts  observed. 

§  3.  THE   ELECTROMAGNETIC   MOMENTUM  AND  THE   PRESSURE  OF  A 

BEAM  OF  LIGHT. 

It  follows  from  Maxwell's  equations  that  there  is  a  tension  in  the 
direction  of  the  lines  of  force,  which  per  unit  area  perpendicular  to  the 
line  is  equal  to  the  density  of  the  energy.  The  pressure  perpendicular 
to  the  lines  of  force  is  just  as  large.  It  follows  that  the  pressure  of  a  beam 
of  light  per  unit  area  is  equal  to  the  electromagnetic  energy  per  unit 
volume.  We  can  now  determine  this  pressure  by  means  of  the  electro- 
magnetic mass  and  momentum.  A  beam  of  light  consists  in  the  present 
theory  of  oscillating  and  advancing  electromagnetic  mass.  The  electric 
force  is  perpendicular  to  the  direction  of  propagation,  sin  #  =  I  and  if 
jj,  =  k  =  i,  then 

E2 

Wi   =  —  . 

47T 

The  momentum  per  unit  volume  is  equal  to 

M 


the  energy  per  unit  volume  will  be 

I  E2c*      H* 


and  the  pressure  per  unit  area  is  equal  to 


27T  /  X  \ 

H  =  HaCoey  U  --) 

then 

-    _  i 

~  2 

and 

*  '  ~  Sir     a  ' 

this  is  the  energy  of  the  beam  per  unit  volume. 
If  k  and  ju  are  both  equal  to  I,  then 

E 

p  =  mic2  =  E,    m  —  Wi  =  -; 

cz 

or  by  differentiation 


m 

dm  =  — . 


471  JAKOB  KUNZ. 

Hence  it  follows  that  a  source  of  radiation,  which  emits  energy,  loses  a 
part  of  its  electromagnetic  mass.  The  sun  loses  yearly  about  io14  tons 
of  electromagnetic  inertia.  On  the  other  hand  if  a  body  absorbs  energy, 
its  mass  must  increase  proportionally  to  the  energy  absorbed,  and  if  an 
electric  charge  is  set  in  motion,  it  will  have  more  magnetic  energy  than 
at  rest.  If  this  electromagnetic  mass  were  granular  and  could  be  broken 
up  into  smaller  units,  such  as  E  =  hn,  then  such  a  unit  would  have  the 
mass  for  yellow  light  mi  =  3iF.io~33,  about  100,000  times  smaller  than 
the  mass  of  the  electron  at  rest. 

§  4.  ON  NEWTON'S  DYNAMICAL  EQUATIONS. 

Every  atom  possesses  at  least  one  electron.  If  the  velocity  of  an 
atom  changes,  the  inertia  will  change  also.  Newton's  dynamical  equa- 
tions require  therefore  a  correction  which  for  all  ordinary  velocities  of 
material  ponderable  bodies  is  insignificant,  but  which  becomes  very 
large,  if  the  velocity  v  approaches  that  of  light.  The  law  of  conservation 
of  mass  does  not  hold  rigorously,  but  the  law  of  conservation  of  momen- 
tum remains  exact. 

The  total  momentum  remains  constant  in  an  enclosed  system  of  heavy 
bodies,  electrical  charges,  magnets,  currents  and  sources  of  light.  If  a 
source  emits  a  beam  in  a  definite  direction,  it  will  lose  momentum  and 
be  driven  in  the  opposite  direction.  If  on  the  other  hand  an  electric 
wave  strikes  a  charge,  or  if  a  beam  is  absorbed  by  a  surface,  then  the 
material  bodies  gain  as  much  momentum  as  disappears  from  the  space. 
A  force  is  defined  in  Newton's  dynamics  by  the  following  equation: 


dt  ' 
but  since 

dM      d(mv) 
dt  dt     ' 

mdv      vdm 

F  == -|- ~ 

dt          dt 

and 

Fdt  =  m  dv  -\-  v  dm. 

If  the  mass  moves  through  space  dl  during  time  dt,  then  the  increase  of 
energy  is  equal  to : 

dl 

dE  =  Fdl  =  F-r.dt  =  Fvdt  =  dmv2  -f  mvdv  =  c*dm, 
at 

dm(c2  —  v2)  =  mv  dv, 

(v2\       m 
I  —  ~i  ]  =  -7  v  dv. 
C   I         C 


THEORY  OF  LIGHT.  472 

This  equation  has  been  integrated  by  Lewis  and  Tolman.     Putting 

v/c  =  x,  we  get: 

dm  _        £  d(i  —  x2) 

m  '         2     I  —  x2 

log  m  =  log  (i  —  x*)~*  +  log  WQ, 
m  i 


hence  we  find  again  for  the  increase  of  the  mass  the  expression  given  by 
relativity. 

The  corrected  equation  of  Newton  holds  not  only  for  the  ordinary 
inert  bodies,  but  also  for  the  radiations  in  a  cavity.  In  a  cavity  bounded 
by  perfect  mirrors,  we  may  find  for  the  radiant  energy  E,  the  expression 

E  =  me2, 

or  the  energy  of  radiation  possesses  inertia.  If  moreover  this  electro- 
magnetic inertia  is  subject  to  gravity,  then  the  weight  of  such  a  cavity 
will  be  equal  to  : 


If  further  the  electromagnetic  mass  is  at  the  same  time  heavy,  then  the 
gravity  of  the  earth  will  exert  on  a  certain  body  a  force  in  a  given  point, 
which  depends  on  the  state  of  motion  or  rest  of  the  body.  An  ordinary 
potential  of  gravity,  as  a  function  of  the  coordinates,  only  exists  no  more, 
for  it  now  depends  on  the  velocity  of  the  falling  body  as  well. 

If  the  electromagnetic  mass  is  subject  to  gravity,  then  a  beam  of  light 
from  a  fixed  star,  passing  through  the  field  of  attraction  of  the  sun,  will 
be  attracted  and  therefore  the  position  of  the  star  will  appear  displaced. 
This  very  important  problem  may  be  solved  by  this  phenomenon  or  also 
by  observations  made  with  pendulums  of  radioactive  substances  which 
are  very  rich  in  electrons.  Let  us  consider  two  geometrically  similar 
pendulums,  the  first  consisting  of  a  radioactive  substance,  such  as  radium, 
the  second  of  non-radioactive  substance.  We  shall  assume  the  weight 
Mg  of  the  two  pendulums  to  be  the  same,  but  the  mass  M  of  the  radio- 
active substance  to  be  m\  +.  m,  where  mi  shall  be  subject  to  gravity,  the 
electromagnetic  mass  m  independent  of  gravity.  The  periods  of  the  two 
pendulums  will  be  _ 


1  2    =    27T M . 

,    Mgs 


473  JAKOB  KUNZ. 

The  radioactive  pendulum  would  have  a  longer  period  than  the  ordi- 
nary one.  I  gr.  radium  contains  about  1/13  mgr.  more  mass  in  the  active 
state  than  after  the  transformations.  In  recent  years  it  has  been  shown 
by  Eotvos  that  for  ordinary  bodies  the  inertia  is  exactly  proportional 
to  the  weight  up  to  io~7.  But  nevertheless  we  have  not  yet  a  direct 
experimental  proof  that  the  electromagnetic  mass  is  subject  to  gravity. 

§  5.  THE  EXPERIMENT  OF  MICHELSON-MORLEY. 

As  there  is  no  independent  medium,  the  motion  of  the  earth  has  no 
influence  upon  geometrical  optics  and  the  result  will  remain  the  same 
whether  we  place  the  interference  apparatus  of  Michelson-Morley  in  the 
direction  of  the  motion  of  the  earth  or  perpendicular  to  it.  Even  if  the 
source  of  light  were  not  connected  with  the  apparatus,  but  were  in 
motion,  as  for  instance  if  the  light  of  canal  rays  were  made  use  of  or  the 
light  of  a  star,  in  no  case  would  we  observe  a  displacement  of  the  inter- 
ference fringes  through  a  rotation  of  the  apparatus.  Here  appears  a 
distinct  difference  between  the  electromagnetic  and  the  mechanical 
emission  theories.  According  to  the  latter  theory  we  should  expect  an 
effect  in  the  experiment  of  Michelson-Morley,  if  the  light  were  incident 
from  a  star. 

§  6.  THE  EXPERIMENT  OF  TRONTON  AND  NOBLE. 

The  energy  of  an  electric  condenser  of  two  plane  parallel  plates  is 
independent  of  the  direction  of  the  motion  of  the  earth ;  this  experimental 
fact  follows  immediately  from  our  assumptions.  In  the  theory  of  an 
independent  ether  however  the  condenser  would  possess  more  energy  if 
the  plates  were  parallel  to  the  velocity  v  of  the  earth,  than  if  they  were 
perpendicular  to  it.  A  charged  and  suspended  condenser  would  produce 
a  couple  in  the  first  position  tending  to  bring  it  into  the  second  position. 

§  7.  ABERRATION  OF  THE  LIGHT  FROM  FIXED  STARS. 

While  the  light  of  a  fixed  star  travels  from  the  objective  A  of  the  tele- 
scope to  0',  the  earth  moves  with  the  velocity  v  from  0  to  0'.  The 
phenomenon  of  aberration  was  always  evidence  in  favor  of  an  emission 
theory  or  led  to  the  assumption  of  a  stationary  ether,  through  which 

the  earth  moves. 

00'  _  v  _  sinfr  _       „ 

$  is  the  angle  of  aberration,  v/c  the  constant  of  aberration  of  the  light 
from  fixed  stars. 


THEORY  OF  LIGHT.  474 

§  8.  THE  EXPERIMENTS  OF  AIRY  AND  FIZEAU. 

As  the  constant  of  aberration  v/c  depends  only  on  v  and  c,  Airy  thought 
that  it  must  change,  if  c  changes.  He  filled  therefore  the  telescope  with 
water  and  expected  a  different  angle  of  aberration,  as  the  velocity  of 
light  in  water  is  equal  to  c/r,  if  r  is  the  index  of  refraction  of  water.  Airy 
found  however  no  change  of  the  constant  of  aberration  and  he  concluded 
that  the  water  carries  the  ether  with  it,  so  that  the  velocity  v  is  diminished 
by  the  same  measure  as  c.  If  the  water  were  carrying  the  ether  with  it 
with  its  own  velocity,  then  no  aberration  would  be  possible,  it  must  there- 
fore communicate  to  the  ether  only  a  fraction  of  its  own  velocity.  If  the 
oscillating  and  advancing  mass  of  a  beam  of  light  falls  upon  a  transparent 
substance  containing  bound  electrons,  these  charges  will  be  set  in  motion 
and  emit  electromagnetic  mass  themselves.  If  moreover  the  substance 
struck  by  light  is  in  motion,  the  electrons  will  be  deviated  from  their 
original  direction  and  oscillate  in  a  new  path.  The  light  emitted  will  be 
perpendicular  to  this  new  direction  and  the  original  beam  of  light  appears 
to  be  deflected  from  the  original  direction. 

A  beam  of  light  strikes  a  column  of  water  with  plane  surfaces,  which 
move  with  constant  velocity  v  perpendicular  to  the  beam  of  light.  Let 
us  consider  in  a  given  point  0  of  Fig.  4  an  electron,  which,  if  the  water  is 
at  rest,  under  the  action  of  the  electric  force  OE,  is  deflected  in  the  direc- 
tion OD.  The  magnetic  force  would  have  no  influence.  If  however 
the  electron  together  with  the  water  is  set  in  motion  with  the  velocity  v, 
then  the  magnetic  field  of  the  light  will  act  upon  the  charge  in  motion 
tending  to  deflect  it  in  the  direction  OF.  The  resulting  deflection  and 
oscillation  will  be  along  OE']  the  new  beam  will  travel  in  a  path  per- 
pendicular to  this  direction,  that  is  from  0  to  0'. 

OD  =  eE, 


<*-¥ 

OF 


this  means  that  the  angle  of  aberration  <£  is  independent  of  the  specific 
properties  k  and  r  of  the  medium.  Hence  Fizeau's  experiment  follows 
immediately. 

The  water  communicates  to  the  beam  a  part  of  its  own  velocity  v,  so 
that  the  beam  travels  in  the  direction  of  v  with  a  velocity  u.     It  will 


475  JAKOB  KUNZ. 

strike  a  point  A  on  the  lower  side  of  the  layer  of  water,  and  be  deflected, 
so  that  $  represents  again  the  angle  of  deviation  between  the  real  and 
the  observed  beam.  Now  we  have 

v  —  u 
sm  a  =  —y-  , 

r,    c  =  Vr, 


sm      =  r  sm  a 


sm  a 

r(v  —  u) 


~  , 

r  C 

This  angle  however  is  independent  of  the  specific  properties  of  the  flowing 
substance  ;  hence  for  the  vacuum  : 

r  =  i,    u  =  o, 

sin  $  =  -, 
c 

;  =  -(»  -  «),     (»  -  w)r>  =  v, 
c/        t/ 


This  is  according  to  Fresnel  and  Fizeau  the  fraction  of  the  motion,  which 
the  flowing  water  communicates  to  the  beam  of  light. 

If  we  observe  a  point  at  rest  through  a  rotating  disc  of  glass,  it  will 
appear  to  be  deflected  from  its  natural  position.  If  we  use  a  Roentgen 
ray  instead  of  a  beam  of  light  then  r  the  index  of  refraction  is  equal  to  I 
and  therefore  u  =  o,  that  is,  we  would  expect  that  Fizeau's  experiment 
gives  a  negative  result  with  Roentgen  rays. 

RECENT  LITERATURE. 

The  present  attempt  at  an  electromagnetic  emission  theory  is  based 
upon  the  works  of  Faraday,  Maxwell,  H.  A.  Lorentz  and  other  investi- 
gators. J.  J.  Thomson  especially  has  in  various  investigations  treated 
the  electromagnetic  field  of  an  elementary  charge  as  something  individual, 
endowed  with  mass,  momentum  and  energy.  He  has  however,  so  far 
as  I  know,  not  extended  the  theory  to  the  critical  phenomena  here 
treated.  Contributions  to  the  present  theory  have  been  made  by  N.  R. 
Campbell  in  his  book  on  modern  electrical  theory,  by  D.  Comstock, 
PHYSICAL  REVIEW,  30,  p.  267,  1910;  R.  C.  Tolman,  PHYSICAL  REVIEW, 

31,  p.  26,  1910;  35,  p.  136,  1912;  O.  M.  Stewart,  PHYSICAL  REVIEW, 

32,  p.  418,  1911,  and  J.  Kunz,  American  Journal  of  Science,  30,  p.  313, 
1910. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
URBANA,  ILLINOIS, 
March  12,  1914. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  IV,  No.  i,  July,  1914.] 


SOME    BRUSH    DISCHARGE    PHENOMENA    PRODUCED    BY 
CONTINUOUS   POTENTIALS. 

BY  STANLEY  P.  FARWELL. 

INTRODUCTION. 

WHEN  there  exists  a  large  difference  of  potential  between  a  wire 
and  neighboring  conductors  such  as  a  similar  and  parallel  wire, 
or  a  coaxial  cylinder,  the  discharge  phenomenon  known  as  corona  is 
likely  to  occur.  For  alternating  differences  of  potential,  this  phenomenon 
has  been  extensively  studied  by  Peek,  Whitehead,  Russell  and  others. 
The  alternating  corona  takes  the  form  of  a  more  or  less  continuous  and 
uniform  bluish  glow  along  the  wire.  The  corona  produced  by  continuous 
potentials  has  not  received  so  much  attention,  presumably  on  account 
of  the  fact  that  its  practical  bearing  on  engineering  problems  is  not  so 
great.  Watson1  and  Schaffers2  have  carried  out  experiments  on  the 
corona  thus  produced.  Watson  has  experimented  on  wires  as  small  as 
0.7  mm.  and  at  pressures  as  low  as  360  mm.  Schaffers  has  worked  with 
cylindrical  fields,  using  wires  as  fine  as  0.006  mm.  and  various  sizes  of 
tube  and  has  determined  the  critical  voltage  for  visual  corona  at  atmos- 
pheric pressure. 

DESCRIPTION  OF  EXPERIMENTS. 

The  writer  has  been  studying  the  corona  as  produced  by  continuous 
potentials  for  wires  from  0.037  mm.  to  1.285  mm.  diameter  and  tubes 
3.50  cm.  and  4.45  cm.  diameter.  The  relation  between  difference  of 
potential  and  current  between  wire  and  tube  has  been  studied  for  at- 
mospheric pressure  for  the  different  sizes  of  wire;  the  critical  voltage  for 
visual  corona  has  been  obtained  for  pressures  from  somewhat  above 
atmospheric  down  to  2.0  mm.  of  mercury  and  the  character  of  the  dis- 
charge noted;  and  the  effect  of  variation  of  voltage  for  a  constant  low 
pressure  has  been  investigated. 

The  object  of  this  paper  is  to  present  especially  some  of  the  phenomena 
observed  at  these  lower  pressures,  the  influence  of  a  short  arc  in  series 
with  the  apparatus  upon  the  character  of  the  discharge,  and  the  increase 
of  pressure  in  the  tube  due  to  the  ionization. 

1  Watson,  Electrician,  Sept.  3,  1909,  Feb.  n,  1910,  Feb.  18,  1910. 

2  Schaffers,  Comptes  Rendus,  July,  1913,  p.  203. 


32  STANLEY  P.  FARWELL. 

INFLUENCE  OF  PRESSURE  UPON  CHARACTER  OF  DISCHARGE. 

The  series  of  photographs  in  Fig.  I  represents  the  change  in  the  dis- 
charge when  the  wire  is  negative  to  the  tube  and  the  pressure  in  the  tube 
is  varied  from  a  low  value  up  to  atmospheric.  The  wire  was  No.  30 
B.  &  S.  (0.26  mm.  diameter)  bare  copper  taken  from  a  coil  obtained  from 
the  manufacturer.  A  glass  tube  25  cm.  long  was  lined  with  a  brass 
sheath,  except  for  a  slit  6  mm.  wide  extending  from  end  to  end,  and  having 
an  internal  diameter  of  3.5  cm.  The  wire  was  stretched  tightly  along  the 
axis,  passing  through  glass  plates  at  the  ends.  The  tube  was  rendered 
air  tight  by  sealing  wax  and  it  could  be  exhausted  through  a  branch  tube 
attached  to  the  side  of  the  cylinder. 

For  the  lowest  pressures,  the  discharge  takes  the  form  of  brilliant  beads 
encircling  the  wire.  Each  has  a  bright  cylindrical  core,  outside  of  which 
is  a  dark  space  which  in  turn  is  surrounded  by  a  purplish  glow  extending 
out  for  some  distance  from  the  wire.  As  the  pressure  is  increased,  the 
difference  of  potential  required  to  produce  a  discharge  increases,  and  the 
number  of  beads  increases.  The  central  nucleus  contracts  and  the  bead 
becomes  more  and  more  like  a  brush  until  finally  there  is  a  line  of  brushes 
along  the  wire.  Each  brush  consists  of  a  bright  spot  on  one  side  of  the 
wire,  with  a  fan-like  purple  glow  spreading  out  from  it,  the  plane  of  the 
fan  being  perpendicular  to  the  axis.  With  the  slit  tube,  the  brushes 
point  in  different  directions  but  if  a  similar  test  be  run  on  a  tube  without 
a  slit  and  one  looks  along  the  wire,  the  bright  nuclei  are  seen  to  lie  all 
in  a  plane,  with  alternate  brushes  on  opposite  sides  of  the  wire,  as  a  general 
rule. 

As  the  pressure  is  raised  toward  atmospheric  the  isolated  brush  type 
of  discharge  gives  place  to  such  a  discharge  as  is  pictured  in  Fig.  I  for 
357.0  mm.  pressure.  An  occasional  brush  is  left,  mixed  up  with  a  more 
or  less  continuous  glow  which  is  very  irregular.  For  atmospheric 
pressure,  the  discharge  looks  like  the  upper  picture.  The  isolated 
brushes  are  very  few,  the  rest  of  the  wire  presents  an  extremely  "messy" 
appearance,  the  glow  is  bright  and  purplish  and  the  discharge  seems  in 
constant  movement. 

For  the  lower  pressures,  a  slight  increase  of  voltage  above  that  required 
to  produce  beads  is  sufficient  to  produce  a  violet  arc-like  discharge  across 
the  gap  between  wire  and  tube  at  one  or  two  points  and  if  this  discharge 
be  allowed  to  continue,  the  wire  will  be  burned  in  two. 

The  photographs  for  261.8  mm.  pressure  in  Fig.  2  show  the  transition 
from  one  form  of  discharge  to  another,  as  it  takes  place  for  somewhat 
higher  pressures.  At  the  critical  voltage,  a  continuous  glow  appears. 
Then  as  the  voltage  is  raised  slightly,  the  glow  becomes  spotted,  followed, 


N^'i!V']  BRUSH   DISCHARGE   PHENOMENA.  33 

at  a  higher  voltage,  by  the  gradual  breaking  up  of  the  glow  into  the 
isolated  brush  form  of  discharge.  Sometimes  this  process  is  not  so 
gradual  as  here  indicated.  Suppose  a  difference  of  potential  be  im- 
pressed of  a  value  above  that  required  to  just  produce  a  glow.  At  the 
instant  of  closing  the  circuit,  one  sees  a  continuous  glow  which  dissolves 
into  the  brush  discharge,  the  brushes  emerging  one  by  one,  until  the 
entire  wire  is  strung  with  them.  The  upper  picture  illustrates  the  regu- 
larity of  spacing  of  the  brushes,  which  will  be  taken  up  later. 

The  characteristic  appearance  of  the  discharge  with  the  wire  positive 
is  that  of  continuous,  uniform,  bluish  glow  of  diameter  little  greater  than 
that  of  the  wire.  Its  appearance  is  not  noticeably  changed  by  changes 
in  pressure,  but  it  gets  brighter  with  increasing  difference  of  potential. 

EFFECT  UPON  DISCHARGE  OF  AN  ARC  IN  SERIES. 

The  effect  upon  the  discharge  of  a  short  arc  in  series  with  the  apparatus 
is  shown  in  Fig.  2  for  a  pressure  of  1 12.6  mm.  When  the  wire  is  positive, 
the  introduction  of  an  arc  causes  the  glow  to  brighten,  increase  in  diameter, 
become  more  purple,  and  more  ill  defined  as  to  boundary.  The  currents 
recorded  on  the  photographs  are  obtained  from  the  deflections  of  a 
D'Arsonval  galvanometer.  When  the  arc  is  introduced,  the  current  so 
obtained  is  much  less  than  one  would  expect  from  the  small  increase  in 
resistance  of  the  circuit  caused  by  the  arc.  Evidently  the  discharge  with 
arc  in  series  is  made  up  of  two  forms  of  discharge  superimposed;  the 
effect  due  to  the  continuous  potential  and  an  alternating  effect  caused 
by  the  oscillations  set  up  in  the  circuit  by  the  arc. 

This  superposition  of  effects  is  clearly  illustrated  when  the  wire  is 
negative.  The  arc  here  causes  a  marked  change  in  the  discharge.  The 
result  is  a  continuous  glow  with  a  few  isolated  brushes  strewn  along  it. 

To  test  out  the  effect  produced  by  the  arc  in  apparently  producing 
oscillations  in  the  circuit,  a  condenser  was  connected  across  the  cylindrical 
field.  The  introduction  of  the  condenser  caused  the  discharge  to  take 
the  same  form  it  had  before  the  arc  was  introduced,  except  for  there  being 
a  few  less  brushes.  When  there  is  a  condenser  thus  in  the  circuit  and  the 
switch  is  closed,  the  transition  from  a  continuous  negative  glow  to  the 
brush  form  of  discharge  is  prolonged.  With  the  condenser  still  in  the 
circuit,  the  disconnection  of  the  impressed  difference  of  potential  gives 
an  opportunity  for  a  discharge  of  the  condenser  across  the  cylindrical 
field.  At  the  instant  the  line  circuit  is  opened,  no  change  in  the  appear- 
ance of  the  brushes  is  noticeable.  Then  as  the  condenser  discharges  and 
its  potential  falls,  there  is  presented  a  "moving  picture"  of  the  stages  of 
the  discharge  down  to  darkness.  This  discharge  was  a  matter  of  several 


34  STANLEY   P.   FARWELL. 

seconds.  As  the  voltage  fell,  the  brush  type  of  discharge  was  main- 
tained: each  regular  arrangement  of  brushes  giving  place  to  another 
regular  arrangement  of  fewer  brushes.  Since  the  resistance  of  the  field 
is  large,  the  condenser  discharge  must  be  of  the  continuous  type. 

DISCHARGE  BETWEEN  PARALLEL  WIRES. 

Two  No.  34  copper  wires  were  placed  parallel  and  2  cm.  apart  inside 
a  tube  of  glass  25  cm.  long  and  the  photographs  of  Fig.  3  were  taken  for 
pressures  less  than  atmospheric.  The  tendency  of  the  negative  wire  to 
show  an  isolated  brush  discharge  and  the  positive  to  give  a  continuous 
glow  is  evident  here.  There  is  evidently  a  tendency  for  the  positive 
sections  of  continuous  glow  to  break  up  into  spots  or  streamers.  For 
constant  pressure,  the  increase  of  the  number  of  sections  of  the  discharge 
with  increase  of  voltage  will  be  noted.  The  spacing  of  the  sections  is 
approximately  regular  and  would  undoubtedly  be  more  so  if  the  wires  were 
more  exactly  parallel  and  stretched  more  tightly  to  make  them  straighter. 

The  two  upper  photographs  show  the  effect  produced  by  an  arc  in 
series.  There  is  no  longer  the  great  difference  between  the  appearance 
of  the  two  wires.  The  negative  wire,  however,  still  shows  a  tendency  to 
discontinuity  of  discharge.  When  the  current  is  sufficiently  great,  violet 
streamers  cross  between  the  wires  as  shown  in  the  upper  picture.  The 
current  indicated  is,  again,  only  the  component  given  by  the  galvano- 
meter. 

SPACING  OF  BRUSHES  AS  A  FUNCTION  OF  THE  VOLTAGE. 

The  slit  tube  previously  described  was  fitted  with  an  arrangement  for 
stretching  the  wire  tighter  and  a  series  of  photographs  was  taken  of  the 
discharge  under  constant  pressure,  with  the  wire  negative  and  varying 
difference  of  potential.  This  series  is  shown  in  Fig.  4.  The  lowest 
picture  shows  the  appearance  of  the  discharge  at  a  voltage  little  higher 
than  that  required  to  produce  visual  corona.  It  will  be  noticed  that 
there  are  many  tiny  brushes  and  no  regularity  of  spacing.  For  a  little 
higher  voltage,  the  number  of  small  brushes  has  decreased  and  there  are 
a  number  of  large  brushes  disposed  at  quite  regular  intervals.  The 
succeeding  photographs  show  the  effect  of  increasing  the  voltage  still 
further.  The  number  of  brushes  continually  increases  and  the  spacing 
is  very  regular.  For  the  lower  voltages,  the  brushes  are  fixed  in  position 
for  a  given  voltage  and  will  always  show  up  in  the  same  position  as  the 
circuit  is  interrupted  and  then  closed  again.  When  the  voltage  ap- 
proaches the  value  at  which  there  will  be  an  arc  between  wire  and  tube, 
each  brush  is  in  constant  movement  back  and  forth  in  a  short  path,  but 
the  number  of  brushes  is  constant  for  a  given  voltage. 


VOL.  IV.l 
No.  i. 


BRUSH   DISCHARGE   PHENOMENA. 


35 


Fig.  5  shows  the  relation  between  difference  of  potential  and  current. 
In  connection  with  this  graph  it  might  be  noted  that  the  critical  voltage 
for  visual  corona  was  2,440. 

It  would  appear  from  a  close  observation  of  the  character  and  spacing 
of  the  brushes  that  there  are  only  certain  voltages  for  which  there  appears 
a  regular  distribution  of  full-sized  brushes.  For  intermediate  voltages, 


16 
15 
14 

12 

I" 

^10 

V 

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/ 

J 

/ 

/ 

/ 

1 

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J& 

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*>*y 

j  — 

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f   Z£   L6  ZJ  id    Z9    5.0    5.1  M  3J   J.4  J5   36  37  38  J9   40  41 
DIFFERENCE  OF  POTENTIAL    IN   KILOVOLTS 

Fig.  5. 

there  is  more  or  less  irregularity  in  the  size  of  the  brushes  and  their  spacing. 
For  the  pictures  of  Fig.  4  an  effort  was  made  to  pick  outjthose  points 
at  which  the  distribution  was  the  most  regular.  Fig.  6  shows,  the  vari- 


IN  10 

*• 

* 


«  i 
I '5 


( 

t 

g 

A    - 

x 

^ 

^ 

r 

1ft 

P^ 

X 

/ 

0 

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r,r 

t  ^ 

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K'f^ 

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r-» 

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Fig.  6. 

ation  with  the  difference  of  potential  of  the  number  of  full-sized  brushes 
and  the  current  per  brush.  When  there  was  a  marked  variation  in  the 
size  of  the  brushes  an  estimate  was  made  of  the  equivalent  number  of 
full-sized  brushes.  These  graphs  clearly  indicate  that  a  definite  relation 
exists  between  the  voltage  and  the  number  of  brushes,  for  a  given  pressure, 
and  that  the  current  per  brush  is  not  a  constant  but  also  varies  with  the 
voltage. 


36  STANLEY   P.   FARWELL. 

The  question  may  be  raised  as  to  whether  the  isolated  brush  form  of 
discharge  may  not  be  due  to  oscillations  in  the  circuit.  In  order  to  make 
it  clear  that  this  is  essentially  a  direct  current  phenomenon,  there  is 
given  below  a  description  of  the  generating  apparatus  used  in  producing 
the  continuous  potentials  and  some  experiments  and  arguments  which 
support  this  view. 

The  source  of  electromotive  force  was  a  battery  of  small  direct-current 
generators,  self -excited  and  connected  in  series.  The  machines  were 
rated  at  500  volts  and  250  watts  and  there  were  thirty  in  all,  giving  15,000 
volts  at  normal  voltage.  The  machines  were  arranged  in  two  sets,  ten 
in  one  and  twenty  in  the  other,  each  set  being  driven  by  its  own  direct 
current  motor.  Variation  of  voltage  was  obtained  by  field  control  of 
the  generators  and  of  one  of  the  motors.  To  prevent  damage  to  the 
machines  through  short-circuits,  a  water  resistance  of  a  rather  large 
value  was  connected  between  the  generating  apparatus  and  the  tube. 
The  negative  terminal  of  the  machines  was  grounded.  Electrostatic 
voltmeters  were  used  to  measure  the  difference  of  potential  and  a  D'Ar- 
sonval  galvanometer  in  connection  with  an  Ayrton  shunt  box  to  give 
the  current. 

The  appearance  of  the  brushes  and  the  current  indicated  by  the  gal- 
vanometer are  constant  for  a  given  voltage,  no  matter  what  combination 
of  machines  are  used  as  the  source  of  potential.  One  of  the  sets  may  be 
used  and  the  appearance  of  the  spots  and  the  voltage  and  current  noted. 
Then  if  the  other  set  be  used  to  give  the  same  voltage  with  a  different 
number  and  speed  of  machines,  the  same  results  are  obtained.  If  there 
were  oscillations  set  up  perhaps  by  sparking  at  the  brushes,  we  would 
not  expect  this  agreement. 

Mention  has  been  made  before  of  the  effect  of  the  introduction  of  a 
condenser  in  parallel  with  the  tube.  To  test  whether  the  current  sent 
through  the  tube  by  the  condenser  in  discharging  was  direct  or  oscillatory, 
another  experiment  was  performed.  The  condenser  was  connected 
across  the  positive  and  negative  bus-bars  to  which  the  generating  ap- 
paratus was  connected  through  the  water  resistance.  Then  a  switch 
connecting  the  machines  to  the  bus-bars  was  closed  as  was  also  a  switch 
leading  to  the  tube.  The  deflection  of  the  galvanometer  was  noted  and 
the  appearance  of  the  brushes.  Then  the  generator  switch  was  opened 
and  the  condenser  discharged  through  the  tube  and  the  galvanometer. 
After  the  switch  was  opened,  the  galvanometer  deflection  gradually 
decreased,  the  rate  of  decrease  of  the  deflection  being  slower  and  slower 
as  the  discharge  proceeded.  The  opening  of  the  switch  caused  no  im- 
mediate change  in  the  brushes,  only  the  gradual  change  already  noted. 


BRUSH   DISCHARGE   PHENOMENA.  37 

That  the  discharge  of  the  condenser  must  be  continuous  is  shown  by  the 
deflection  of  the  galvanometer  and  it  can  be  further  proved  by  a  rough 
calculation.  Assuming  the  resistance  of  the  cylindrical  field  as  given 
by  E/I  and  taking  a  set  of  values  of  E  and  I  for  the  comparatively  low 
pressures  at  which  the  brushes  are  best  formed,  we  obtain  R  =  1.83 
X  10  ohms.  Assuming  the  very  large  value  of  o.i  henry  for  the  in- 
ductance of  the  circuit,  and  the  approximate  value  of  2  mf.  for  the 
capacity,  we  find  the  R  is  about  4.1  X  io4  times  as  great  as  ^^L/C 
and  hence  it  is  clear  that  the  condenser  discharge  must  be  of  the  con- 
tinuous type. 

By  running  wires  from  the  terminals  of  an  induction  coil  to  the  central 
wire  and  the  tube  and  then  adjusting  the  discharge  points  on  the  coil 
to  such  a  distance  that  a  silent  discharge  took  place  between  them,  it  was 
possible  to  obtain  an  almost  uniform  hazy  glow  along  the  wire.  But 
no  effect  could  be  obtained  like -the  uniformly  spaced  brush  discharge. 

It  is  well  known  that  an  arc  is  the  source  of  electrical  oscillations  and  it 
has  been  shown  by  a  previous  figure  that  a  short  arc  in  series  with  the 
tube  disturbs  the  brushes  due  to  the  direct  current  by  the  superposition 
of  an  alternating  current  effect  so  that  the  glow  becomes  more  or  less 
uniform  and  the  difference  in  the  appearance  of  the  glow  for  different 
polarities  becomes  much  less.  So  the  introduction  of  an  oscillatory 
current  acts  to  suppress  the  isolated  brush  form  of  discharge  and  not  to 
cause  it. 

The  difference  between  positive  and  negative  electricity  is  hardly  better 
demonstrated  by  any  other  phenomenon.  It  should  be  stated  here, 
however,  that  Peek1  by  a  stroboscopic  method  has  also  observed  "more 
or  less  evenly  spaced  beads"  on  the  negative  wire  when  there  was  corona 
between  parallel  wires  caused  by  an  alternating  difference  of  potential 
of  80,000  volts  at  atmospheric  pressure.  The  wires  used  by  Peek  were 
0.168  cm.  in  diameter,  spaced  12.7  cm.  apart. 

EFFECT  OF  MAGNETIC  FIELD. 

A  strong  horseshoe  electromagnet  was  placed  in  various  positions  with 
its  poles  against  the  tube  and  the  effect  upon  the  various  forms  of  dis- 
charge of  making  and  breaking  the  magnet  circuit  was  observed.  No 
change  could  be  noted  in  the  appearance  of  the  discharge  or  the  current 
flowing. 

VARIATION  OF  PRESSURE  IN  TUBE  WITH  VOLTAGE. 

A  No.  36  B.  &  S.  copper  wire,  0.135  mm.  in  diameter,  was  stretched 
tightly  along  the  axis  of  a  brass  tube  4.45  cm.  in  diameter  and  closed  at 

1  Proc.  A.  I.  E.  E.,  Vol.  31,  No.  6,  p.  1123  and  Plate  LXV. 


STANLEY   P.   FARWELL. 


[SECOND 

[SERIES. 


the  ends  by  glass  plates  through  which  the  wire  passed.  A  small  branch 
tube  was  soldered  to  the  side  of  the  main  tube  and  from  it  connection 
was  made  to  an  air-pump.  An  open  manometer  of  small  bore  con- 
taining a  light  oil  was  connected  to  the  side  of  the  branch  tube.  Every- 
thing was  rendered  airtight  after  disconnecting  the  manometer  and  the 
tube  was  exhausted.  Then  dry  air  was  gradually  admitted  through  a 
tube  containing  soda-lime  and  a  wash-bottle  containing  concentrated 
sulfuric  acid,  until  the  pressure  was  again  atmospheric,  744.0  mm.  in 
this  case.  The  manometer  was  again  connected  and  various  differences 
of  potential  impressed. 

As  soon  as  the  voltage  reached  the  critical  value  to  cause  an  appreciable 
current  to  flow,  a  jump  in  the  columns  of  the  manometer  was  apparent. 
This  jump  occurred  lower  for  the  wire  negative  and  it  was  difficult  to 
tell  just  the  voltage  at  which  it  began.  When  the  wire  is  negative,  any 
little  dust  particle  on  it  will  be  sufficient  to  start  a  discharge  at  a  lower 
voltage  than  would  be  required  to  cause  a  general  glow  along  the  whole 
wire.  But  for  the  wire  positive,  the  critical  point  is  very  marked  and  the 
jump  occurs,  as  closely  as  one  can  judge,  at  the  same  time  that  a  faint 
bluish  glow  is  seen  along  the  wire.  Fig.  7  shows  the  increase  in  the 


Is 

I" 


DIFFERENCE  OF  POTENTIAL    IN  KILOVOLTS 


Fig.  7. 


pressure  as  the  voltage  is  raised.  This  graph  has  exactly  the  same  ap- 
pearance as  the  graph  plotted  between  voltage  and  current,  as  one  might 
expect  from  the  theory  of  the  conduction  of  electricity  through  gases. 
It  will  be  noted  how  the  curves  for  the  two  polarities  cross  at  low  voltages 
and  that  the  increase  of  pressure  for  a  given  voltage  is  greatest  for  negative 


PHYSICAL  REVIEW,  VOL.  IV.,  SECOND  SERIES. 
July,  1914- 


PLATE  I 
To  face  page  38. 


10160  Volte — — -   3.62  *    10     Amp. 737.6  mm, 


3500  Volts —  —   7,63  x    10~    Amp, 


112.6  mm- 


2200   Volte 


3.38   x  10^  Amp. -—.-      75*7  mm. 

•i      10     il     12     1:5     It     1.1     16     17     18     10    20    21" "23     23    2* 


1600    Volts 


'  1  '  2     :s      I- 
Bffliitfiilimiuiilmi  ..'" 


—   3.62   *   10     Amp* — 58.0  mm. 

•  »     n»    ii    12    i;j    u    l'»    10    17    IB    19   20   5r"5"2-55 


'  1800  Volte 


1.83    x  10"* Amp. ~    — —      34.3  ran. 

12      1.1     U     !.">     in    17     IB     1«    20    21  "22     23    24 


600  Volts 6.39   x    10~    Amp. .— -—        9.9  ram. 

**  WIPJ2  NEGATIVE:    CHANGES  WITH  VOLTAGE  AMD  PRESSURE  ## 

Fig.  1. 
STANLEY   P.  FARWELL.  :J 


PHYSICAL  REVIEW,  VOL.  IV.,  SECOND  SERIES. 
July,  1914- 


PLATE  II 
To  face  page  38. 


Negative  Brush  Discharge- -1450  volts — 4.33  x  10  amp. 46.9  mm 


Negative!    Final   Form- 4750  volts — 1.89   x  10  amp. — 261«8  mm 


Negative:    Transition  Stage-4460  volts-l*24  x   10  amp. — 261.8  mm 


Negative:    Transition  Stage-4210  volta-0.72  x  10~4amp.--261.8  rani. 


Negative:    With  Arc 4110  volts — 2.23  x  10  amp. — 112.6  mm, 


Negative:    No  Arc -3950  volts — -4.65  x   10  amp. — 112.6  mm 


Positive:    With  Arc 4100  volts — 2.17  x  l6"\mp. — 112.6  mm 


Positive:   No  Arc .-.-.—  4010  volts-^3.79  x  lO^arap. — 112«6 

EVOLUTION  OF  BRUSH  FORM  OF  NEGATIVE  DISCHARGE 

and 
,  EFFECT  OF  ARC   IN  SERIES  UPOH  FORM  OF  DISCHARGE 


Fig.  2. 
STANLEY   P.  FARWELL. 


PHYSICAL  REVIEW,  VOL,  IV.,  SECOND  SERIES 
July,  1914. 


PLATE  III 
To  face  page  38. 


Arc  in  Series — 8000  Volts — 1.80  x  lO'^Arap. — S12.2  mm* 


Arc  in  Series — 8000  Volts — 1.14  x  1(T*  Amp.—  512.2 


No  Arc- 


•8000  Volts— 2«S§  x  10"**  Amp. —312, 2  nan, 


Ho  Arc 8700  Volts- 


•450.0  mm. 


Ho  Arc  ---  -  -----  -8400  Volte  -----  ;—  «--  —  -.~~~-~4g0,Q 

SOME   FORMS   OP  DISCHARGE  BETWEEN   PARALLEL  WIRES 


Wires-0.165  mm.  -2  cm.   apart~25  cm.   long 
Upper  Wire^is^Negative 


Fig.  3. 
STANLEY    P.  HARWELL. 


PHYSICAL  REVIEW,  VOL.  IV.,  SECOND  SERIES 
July,  1914- 


PLATE  IV 
To  face  page  38. 


3940  Volts    -----    12.2  x   10~4Amp 


3870  Volts 10,0  x   10"^ Amp, 


3550  Volte   — —  4.65  x   10 


3370  Volte   -— —   3*37  x   10~4Amp, 


2800  Volts   — — -   1.03  x   10~4Amp, 


2700  Volts 

nnL.L.LLLl., 


2500  Volts  -•--.—      .33  x  lO~4Amp. 
WIRE  NEGATIVE—PRESSURE  CONSTANT  AT   119.3  ma. 
EFFECT  OF  VARIATION  OF  VOLTAGE  UPON  DISCHARGE 


Fig.  4. 

STANLEY   P.  FARWELL. 


NoTi!V>]  BRUSH   DISCHARGE   PHENOMENA.  39 

polarity  of  the  wire  during  the  greater  part  of  the  range.  The  crossing 
of  the  curves  is  typical  of  the  voltage-current  graphs. 

In  addition  to  the  sudden  jump  at  closure  of  the  circuit  there  is  a 
gradual  increase  of  pressure  due  to  the  heating  effect  of  the  current  and 
hence  care  was  taken  to  read  the  heights  of  the  columns  of  liquid  as  soon 
as  possible  after  the  circuit  was  closed. 

The  work  upon  which  this  paper  is  based  was  performed  in  the  labor- 
atory of  physics  at  the  University  of  Illinois  under  the  direction  of  Dr. 
Jacob  Kunz,  asst.  prof,  of  physics.  To  him  and  to  Prof.  E.  B.  Paine, 
of  the  electrical  engineering  department,  the  writer  wishes  to  acknowledge 
his  indebtedness  for  many  helpful  suggestions  as  to  the  conduct  of  this 
work. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
April,  1914. 


[Reprinted  from  SCIENCE,  N.  8.,  Vol.  XL1L,  No. 
1072,  Pages  93-94,  July  16,  1915} 


THE    DIFFUSION     OF    GASES     AT     LOW     PRESSURES 
MADE  VISIBLE  BY  COLOR  EFFECTS 

AN  interesting  and  instructive  experiment 
for  the  lecture  table  is  to  connect  a  discharge 
tube  AC,  which  is  about  one  meter  or  more 
in  length  and  which  has  the  exhaust  nipple  at 
one  end,  to  a  pump  that  will  give  a  Geissler 
vacuum — an  oil  Geryk  pump  will  answer  very 
well.  Between  the  pump  connection  M  and 
the  valve  0  that  closes  the  tube  there  should 
be  fused  a  side  branch  N  also  having  a  valve. 
Connect  N  by  a  rubber  tube  to  some  source  of 
gas  other  than  air,  e.  g.t  ordinary  illuminating 
gas.  The  connection  at  M  should  be  made 
direct  to  the  pump.  Connect  A  and  C  to  the 
terminals  of  an  induction  coil  that  will  give 
a  spark  in  air  five  or  more  centimeters  long. 

To  operate,  close  the  valve  in  the  branch  N, 
open  0  and  evacuate  the  discharge  tube  to 
the  point  where  on  sparking  the  characteris- 
tic strisB  show  distinctly.  It  is  immaterial 
whether  A  or  C  is  the  cathode,  or  whether  the 
discharge  is  unidirectional.  Now  close  the 
valve  0,  and,  with  the  pump  still  running, 
open  N  partly,  allowing  illuminating  gas  to 
be  drawn  by  the  pump  through  the  branch 
OM,  thus  displacing  the  air  by  the  gas.  By 
closing  N,  pumping  and  later  admitting  more 
gas,  every  trace  of  air  may  be  washed  out  of 


FIG,  1. 

the  tube  leading  up  to  0.  Now  with  N  closed 
allow  the  pump  to  run  for  a  few  seconds  until 
it  is  judged  that  the  pressure  in  the  connect- 


ing  tube  M  0  is  about  that  in  the  discharge 
tube  A  0. 

At  this  stage  everything  is  in  readiness  for 
the  experiment,  namely,  the  diffusion  of  gases 
at  low  pressures  made  visible  by  the  color  ef- 
fect. The  well-known  characteristic  color  of 
the  discharge  in  the  case  of  residual  air,  con- 
taining possibly  some  water  vapor,  is  orange 
red.  To  now  introduce  the  illuminating  gas 
open  the  valve  0  for  a  moment,  then  close  it. 
The  end  0  of  the  discharge  tube  is  instantly 
filled  with  a  beautiful  greenish-white  color 
characteristic  of  illuminating  gas.  This  color 
will  diffuse  slowly  towards  A.,  each  color  pal- 
ing out,  and  after  three  or  four  minutes  the 
discharge  throughout  the  tube  will  assume  a 
uniform  grayish  hue.  The  rate  of  diffusion 
is  surprisingly  slow  and  of  course  depends 
upon  a  number  of  factors,  e.  g.,  the  gas  pres- 
sure in  the  tube,  the  pressure  of  the  gas  that 
is  admitted,  the  ionization  within  the  tube 
due  to  the  discharge  passing  through  the  tube, 
the  amount  of  moisture  present,  etc. 

If  now  the  gas  connection  at  N  be  removed 
and  this  stem  opened  to  the  air  the  pump  and 
connections  may  be  freed  of  gas  and  the  in- 
verse experiment  performed;  namely,  that  of 
introducing  a  small  quantity  of  air.  The  re- 
sulting orange  red  color  and  its  diffusion 
through  the  grayish  hue  of  the  illuminating 
gas  is  even  more  striking  than  the  first. 

The  success  of  the  experiment  depends 
largely  upon  the  skill  of  the  operator  in  prop- 
erly proportioning  the  quantity  of  gas  to  be 
introduced.  It  is  a  very  simple  experiment  to 
perform. 

OHAS.  T.  KNIPP 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
June  2,  1915 


(Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  VI,  No.  2,  August,  1915] 


ON  THE   PRESENT  THEORY  OF   MAGNETISM. 

BY  JAKOB  KUNZ. 


~^HE  electron  theory  seems  to  account  for  the  magnetic  phenomena 
in  a  very  direct  way.  Indeed  we  have  only  to  assume  that  the 
molecular  currents  of  Ampere,  which  form  the  elementary  magnets,  are 
revolving  electrons  in  order  to  express  Ampere's  theory  of  magnetism 
in  terms  of  the  electron  theory.  Nevertheless  it  was  only  on  the  basis  of 
the  researches  of  P.  Curie  that  P.  Langevin  was  able  to  account  for  the 
difference  in  diamagnetism  and  paramagnetism.  Curie  found  that  the 
diamagnetic  susceptibility  is  independent  of  the  temperature  while  the 
paramagnetic  susceptibility  is  inversely  proportional  to  the  absolute 
temperature.  Langevin  concluded  that  there  is  a  fundamental  difference 
between  diamagnetic  and  paramagnetic  properties.  In  Langevin's 
theory  the  diamagnetism  is  a  characteristic  property  of  each  atom  which 
contains  a  certain  number  of  revolving  electrons.  If  the  resultant 
magnetic  moment  of  these  electrons  for  an  external  point  is  zero,  then 
the  body  is  diamagnetic,  the  action  of  an  external  magnetic  field  consists 
in  a  change  of  the  orbit,  giving  rise  to  the  diamagnetic  modification  of 
the  atom.  If  the  revolving  electrons  possess  a  resultant  magnetic 
moment,  the  body  is  paramagnetic.  Matter  in  all  its  forms  is  dia- 
magnetic; paramagnetism,  whenever  it  appears,  covers  as  it  were  the 
diamagnetism,  and  there  is  no  transition  between  the  two  distinct 
groups.  We  shall  add  a  short  deduction  of  the  diamagnetic  suscepti- 
bility. 

We  consider  in  a  diamagnetic  gas  an  atom  with  an  electronic  orbit,  of 
radius  r,  the  electron  e  revolving  with  velocity  v,  in  a  plane  perpendicular 
to  the  magnetic  field.  The  moment  will  be  equal  to  M  =  Trr2(e/T) 
without  magnetic  field;  if  a  field  H  is  applied,  the  time  of  vibration  T 
and  the  angular  velocity  will  change,  so  that 

dM  =  e-7r\-—dr  —  —  dTj  , 

or  neglecting  the  first  part 

dT 


114  JAKOB  KUNZ. 

mv2  mv2 

—  =  /.f  or/  =  --, 

mv2  mv2  Hev       mv2       Hev 

-T  =  fr'  ~  Hev;  -^-  =  /  -    —     =  ~r       -- 

wz;2       Hev 


[i         i  1       He 
r^2  ~"  T^J  =  ~f' "' 

dT  _  dT  _    He 

m^  T2  ~  He]   T2  ~  4irm' 

dM  =   — —  H. 

4m 

If  there  are  N  orbits  per  unit  volume  and  if  the  axes  are  uniformly  dis- 
tributed in  all  directions,  then  we  have 

e2r2N  Tl  e2r2N 

M  =  — H ,  or  k  =  — . 

I2m  I2m 

Apparently  N  and  r  are  independent  of  the  temperature.  This  theory 
of  Langevin  of  the  diamagnetic  susceptibility  k  is  at  the  same  time  the 
theory  of  the  Zeeman  effect. 

In  order  to  find  the  expression  for  the  paramagnetic  susceptibility  fo 
a  gas,  we  shall  use  a  method  quite  different  from  that  of  Langevin.  Let 
the  angle  between  an  external  magnetic  field  H  and  the  direction  of  the 
moment  M  of  an  elementary  magnet  be  equal  to  a,  the  work  required 
in  order  to  rotate  the  magnetic  particle  from  the  direction  H  into  its 
present  direction  will  be  equal  to  W  =  —  MH  cos  a  +  C;  the  heat  of 
the  gas  will  change  by  this  amount,  and  in  order  to  keep  the  temperature 
constant,  we  have  to  add  a  quantity  of  heat  Q  =  —  W  =  MH  cos  a, 
and  the  increase  of  entropy  will  be  equal  to  S  =  (Q/T)  =  (MH  cos  a/71) ; 
and  this  entropy  will  be  proportional  to  the  lograithm  of  the  probability 
P  that  we  find  the  magnet  in  the  direction  a 

MH  cos  a 
S  =  R  log  P  +  const.  = , 

M H  cos  a 


_ 

and  the  number  of  magnets  which  are  found  in  an  angular  interval  da 
will  be  proportional  to  P,  or 

MHcosa 
dn  =  Ke —  -dco, 


VOT    VT  1 

No  2     J  ON  THE  PRESENT  THEORY  OF  MAGNETISM.  115 

where 

du  =  27r  sin  a  da, 

MH  cos  a 

dn  =  Ke ^= — 2ir  sin  a  da, 

J\l 

the  total  number  N  of  molecules  per  unit  volume  will  be 

N  =  2irK  f   eacosasinada, 
where  we  put  a  for  (MH/RT), 

N  =  — —  sin  ha 
a 

and  the  intensity  of  magnetization  3?  becomes: 

M  cos  a  dw 
'  cos  ha 


sin  fia 

The  maximum  value  of  the  intensity  of  magnetization  $m  =  MN,  hence 
m      i\        _     /i  2  4 


Neglecting  the  higher  powers  of  a  =  MH/RT  we  find 

9  =  3  --- 

x?          ^3RT- 


that  is,  the  paramagnetic  susceptibility  is  inversely  proportional  to  the 
absolute  temperature;  that  is  the  rule  of  Curie. 

EXPERIMENTAL  FACTS. 

The  phenomena  are  far  more  complicated  than  the  theory  of  Langevin 
indicates.  The  investigations  of  H.  DuBois,  K.  Honda,  M.  Owen, 
Kamerlingh  Onnes,  P.  Weiss,  A.  Perrier  and  others  have  revealed  a  very 
large  variety  of  phenomena,  in  which  the  rules  of  Curie  are  altogether 
exceptions  so  that  we  have  to  extend  or  abandon  the  present  theories. 

The  diamagnetic  susceptibility  should  be  an  atomic  property,  which 
is  independent  of  temperature,  of  a  change  of  state,  of  a  polymorphic 
transformation  or  of  chemical  combination.  This  is  not  the  case. 
For  instance,  the  diamagnetic  susceptibility  of  amorphous  carbon,  of  Cu, 
Zn,  Zr,  Cd,  3?n>  Sb,  Te,  Tl,  3,  Pb,  Bi,  decreases  with  increasing  tempera- 
ture, k  in  the  melting  of  Ag,  Sn,  Sb,  Ga,  Ge,  Au,  Hg,  Tl,  Pb,  Bi  changes 


I  1 6  JAKOB  KUNZ. 

discontinuously.  In  the  polymorphic  transformation  of  C,  S,  Sn,  and  Tl 
the  susceptibility  changes  abruptly,  even  the  sign  changes  in  the  poly- 
morphic transformation  and  during  the  melting  process  of  tin.  In  the 
case  of  boron  (0-400°  C.),  diamond,  silver  and  iodine  (0-114°)  the  dia- 
magnetic  susceptibility  increases  with  the  temperature.  There  are  only 
a  few  elements  whose  diamagnetic  k  remains  constant  within  a  certain 
interval  of  temperature;  the  diamagnetic  susceptibility  of  an  inorganic 
compound  is  not  an  additive  property.  Oxygen,  for  instance,  is  a 
strongly  paramagnetic  element,  but  if  it  combines  with  the  paramagnetic 
elements  of  Be,  Mg,  Al,  Mo,  W,  Th,  it  forms  diamagnetic  oxides.  And 
in  general  the  diamagnetic  and  paramagnetic  properties  depend  so  much 
on  physical  and  chemical  influences,  that  one  might  be  inclined  to  ascribe 
them  to  electrons  which  are  revolving  on  the  surface  of  the  atom.  In 
organic  compounds,  at  all  events,  it  has  been  shown  by  P.  Pascal  that 
the  molecular  susceptibility  X  is  an  additive  property  of  the  atomic 
susceptibility.  Oxygen  in  these  compounds  may  be  para-  or  dia- 
magnetic. In  more  complicated  compounds,  the  structure  has  a  great 
influence  on  X.  The  diamagnetic  constants  are  on  the  whole  not  smaller 
than  the  positive  paramagnetic  values. 

The  diamagnetic  susceptibility  of  graphite  is  greater  than  the  para- 
magnetic susceptibility  of  such  an  element  as  manganese,  one  of  the 
strongest  paramagnetic  elements;  charcoal,  bismuth  and  antimony  have 
also  large  negative  susceptibilities.  Besides  in  the  crystals  of  graphite 
and 'antimony  k  varies  with  the  direction  of  the  axes.  All  these  facts 
seem  to  indicate  that  what  we  observe  is  the  difference  between  a  positive 
and  negative  magnetism. 

A  similar  variety  of  phenomena  is  observed  in  paramagnetism. 
Oxygen  follows  Curie's  law  at  ordinary  and  at  higher  temperatures,  but 
at  lower  temperatures  the  susceptibility  varies  inversely  as  the  square 
root  of  the  absolute  temperature  and  finally  probably  becomes  constant. 
Over  certain  intervals  of  temperature  the  susceptibility  remains  constant 
in  the  elements:  Na,  Al,  K,  V,  Cr,  Nb,  W,  Os,  and  even  increases  with 
increasing  temperature  in  the  case  of  Ti,  V,  Cr,  Mn,  Mo,  Ru,  Rh,  $r,  Th. 
The  ferromagnetic  metals  above  the  critical  temperature,  where  the 
ferromagnetism  disappears,  seem  to  follow  Curie's  law,  probably  with 
the  exceptions  of  the  compounds  Fe3O4  and  pyrrhotite. 

An  extension  of  Langevin's  theory  is  necessary  both  for  the  dia- 
magnetic and  the  paramagnetic  susceptibility.  In  the  first  place,  in 
Langevin's  theory  it  is  silently  assumed  that  the  moments  of  the  ele- 
mentary magnets  are  independent  of  the  temperature.  This  assumption 
is  by  no  means  self-evident.  The  electrons  revolve  in  the  outer  layers 


NOL  aT1']  ON  THE  PRESENT  THEORY  OF  MAGNETISM.  I  I  7 

of  the  atoms  probably  and  the  moment  of  a  molecule  is  the  resultant 
of  the  moments  of  the  atoms.  With  increasing  temperature  we  have 
reasons  to  believe,  the  atoms  share  the  energy  of  temperature  agitation 
and  the  resultant  moment  of  the  molecule  may  be  affected.  Besides  the 
fact  that  the  diamagnetic  susceptibility  changes  abruptly,  in  polymorphic 
transformations,  in  changes  of  state,  in  chemical  transformations, 
indicates,  that  the  diamagnetism  is  not  simply  an  additive  atomic  prop- 
erty. In  general  we  have  to  put: 

M  =  M0f(T). 

In  the  second  place  Langevin's  theory  of  paramagnetism  applies 
only  to  gases  and  dilute  solutions.  The  resultant  magnetic  moment  per 
unit  volume  depends  only  on  the  directing  power  of  the  field  and  on  the 
"scattering"  power  of  the  temperature  agitation.  The  equilibrium 
between  these  two  effects  leads  to  Curie's  rule.  But  as  soon  as  we  con- 
sider a  more  condensed  state  of  aggregation,  the  molecules  will  exert  an 
influence  on  each  other,  and  this  influence  for  crystals  will  vary  in 
different  directions.  P.  Weiss  has  indeed  extended  Langevin's  theory 
to  ferromagnetic  substances  by  adding  to  the  external  field  H  an  internal  or 
molecular  field  N$>  which  is  proportional  to  the  intensity  3  of  magnetiza- 
tion. In  this  way  P.  Weiss  was  able  to  explain  a  large  number  of  phe- 
nomena of  ferromagnetic  crystals.  A  similar  influence  however  must 
exist  in  paramagnetic  solid  and  liquid  substances.  The  mutual  action 
of  the  molecules  will  be  a  certain  function  of  the  temperature  f(T)  and 
will  in  general  oppose  the  tendency  of  the  external  field  to  direct  the 
elementary  magnets,  just  as  the  temperature  agitation;  so  that  the 
energy  of  the  opposing  forces  may  be  written  in  the  form;  RT 

K/T  f(  7""^  TT 

the  parameter  a  will  now  be  equal  to  p^   ,    r  /^N  and  3  will  become : 

Kl 

cos  ha 


or  approximately: 


[M,f(T)fN 


if  f(T)  is  a  constant,  for  instance,  equal  to  I  and  f\(T)  also  a  constant 
QR,  then  we  find 


Il8  JAKOB  KUNZ.  [SECOND 

LoERIES. 

MfN 


BR) 

or 

k(T  +  6)  =  constant, 

a  result  which  has  been  deduced  by  E.  Oosterhuis1  from  Planck's  theory 
of  quanta  of  energy  by  entirely  different  considerations.  At  very  low 
temperatures  the  specific  heat  of  all  substances  seems  to  approach  zero, 
the  coefficient  of  expansion  approaches  zero  also,  the  electrical  conduc- 
tivity of  metals  becomes  very  large,  if  not  infinite,  the  thermal  conduc- 
tivity increases  rapidly.  All  these  properties  can  be  explained  by  the 
assumption  that  at  these  very  low  temperatures  in  the  neighborhood  of 
the  absolute  zero  the  molecules  gradually  lose  their  mobility,  and  a  given 
substance  at  absolute  zero  is  a  real  solid  body,  as  it  were  one  large 
molecule,  where  the  molecular  mobility  has  disappeared;  that  means 
that  the  influence  of  the  temperature  agitation  of  the  individual  ele- 
mentary magnets  becomes  weaker  and  weaker  and  that  we  can  not  even 
define  the  molecular  magnet,  because  the  whole  system  of  magnets  is  as 
it  were  solidified,  so  that  even  at  the  absolute  zero  saturation  of  a  sub- 
stance is  impossible  and  that  the  influence  of  temperature  becomes 
smaller  and  smaller  or  the  paramagnetic  susceptibility  becomes  constant. 
This  seems  to  be  the  tendency  of  solid  oxygen. 

If  now  at  the  lowest  temperatures  the  function  ([f(T)]2/RT  +/i(r)) 
is  a  constant,  and  at  rather  high  temperatures  is  equal  to  i/T  and 
changes  continuously  from  one  extreme  to  the  other,  then  it  will  in 
intermediate  temperatures  be  approximately  equal  to  i/T1*,  and  for  this 
interval  we  shall  have: 

MfN 

3r»  ' 

a  result  which  has  been  obtained  by  H.  Kamerlingh  Onnes  and  A. 
Perrier  for  liquid  and  solid  oxygen.  The  formula  k(T  +  0)  =  C  or 
X(T  +  9)  =  C,  where  X  is  the  molecular  susceptibility  will  be  tested 
by  means  of  measurements  made  in  Leiden2  on  manganese  sulfate. 

In  the  next  place  the  free  electrons  will  be  considered  as  contributing 
to  the  diamagnetic  susceptibility.  It  has  been  shown  by  H.  E.  Dubois 
and  K.  Honda  that  the  diamagnetic  susceptibility  of  amorphous  carbon, 
Cu,  Zn,  Cd,  In,  $,  Sb,  Te,  Tb,  Pb,  Bi,  Sb  decreases  with  increasing  tem- 
peratures. The  strongest  diamagnetic  metals  are  Sb  and  Bi,  which 
show  also  a  very  large  Hall  effect.  The  magnetic  field  seems  to  act  on 

1  Die  Abweichungen  vom  Curie'schen  Gesetz  im  Zusammenhang  mit  der  Nullpunktsenergie, 
Phys.  Zeitschrift,  Vol.  XIV.,  p.  862,  1913. 

2  Leiden,  Comm.  No.  1326. 


VOL.  VI.l 
No.  2. 


ON  THE  PRESENT  THEORY  OF  MAGNETISM. 


119 


MnS044H20 

MnS04 

Tabs. 

X-  106  Abs. 

Cioio 

©  =  1.18 

Tabs. 

^•106 

CK>™ 

©  =  26.5 

288.7 

66.3 

1.92 

293.9 

82.8 

2.82 

169.6 

111.5 

1.905 

169.6 

144.2 

2.83 

77.4 

247 

1.93 

77.4 

274.8 

2.85 

70.5 

270 

1.93 

64.9 

314.5 

2.87 

64.9 

292 

1.93 

20.1 

603 

2.82 

20.1 

914 

1.94 

17.8 

627 

2.78 

17.8 

1,021 

1.94 

14.4 

636 

2.60 

14.4 

1,233 

1.92 

the  free  electrons  so  that  they  move  in  spirals  or  circles  and  produce 
diamagnetism.  E.  Schrodinger1  found  for  the  contribution  k  of  the 
diamagnetism,  made  by  the  free  electrons: 

i  e2 

k  =  -i-XW, 
3  w 

where  N  is  the  number  of  free  electrons  per  unit  volume,  and  X  the  mean 
free  path.  The  effect,  calculated  in  this  way,  is  100  times  too  large  for 
silver  and  copper,  which  seems  to  be  another  argument  against  the 
"free"  electrons  in  metals.  Nevertheless  the  action  of  temperature 
on  diamagnetism  and  the  fact  that  Sb  and  Bi  have  a  large  Hall  effect 
and  a  large  negative  magnetism  indicate  that  the  conduction  electrons 
contribute  somewhat  to  the  diamagnetism. 

THE  PERIODIC  SYSTEM  OF  THE  ELEMENTS  AND  THEIR  MAGNETIC 

PROPERTIES. 

The  elements  may  be  arranged  in  series  according  to  the  atomic 
weights  in  different  ways.  A  certain  periodicity  between  atomic  weights 
and  magnetic  properties  always  appears.  If  the  atomic  weights  are 
represented  by  abscissae  and  the  magnetic  susceptibilities  as  ordinates, 
the  curve  obtained  is  of  a  most  irregular  character,  representing  seven 
distinct  maxima,  among  which  that  of  the  iron  group  is  by  far  predomi- 
nating. If  only  the  sign  of  the  magnetic  properties  is  taken  into  account, 
one  gets  the  best  representation  perhaps  by  the  method  of  the  helix 
due  to  B.  K.  Emerson,  which  is  given  in  Fig.  i. 

The  strongly  magnetic  groups  appear  on  a  diameter,  where  we  find 
Fe,  Ni,  Co,  then  Pd,  Ru,  Rh,  then  Gd,  En,  Sm,  then  Pt,  3r,  Os.  Moving 
on  the  spiral  from  iron  to  the  right,  we  meet  Mn  and  Cr,  elements  which 
are  paramagnetic,  but  whose  strongly  magnetic  properties  appear  only 
in  some  of  their  alloys  and  compounds  such  as  the  Heusler  alloys,  manga- 

1  Kinetische  Theorie  des  Magnetismus,  Sitz.  Ber.  der  K.  Akademie  der  Wissenschaften, 
Ila,  Bd  CXXL,  p.  1305,  1912. 


I2O 


JAKOB  KUNZ. 


[SECOND 

[SERIES. 


nese-antimony,  manganese- tin,  manganese-zinc,  Cr5O9.  On  the  right 
hand  side  from  the  ferromagnetic  elements,  there  are  paramagnetic 
elements,  on  the  left  hand  side  the  diamagnetic  elements.  Opposite  to 
the  magnetic  metals  there  are  the  inert  gases,  which  seem  to  be  weakly 
diamagnetic.  On  the  right-hand  side  of  the  inert  gases  we  find  the  alkali 
metals  whose  weakly  paramagnetic  properties  are  not  yet  sufficiently 
known.  The  strongly  magnetic  metals,  cobalt,  nickel  and  iron,  belong 
to  the  elements  with  minimum  compressibility,  with  most  complex 


Jf, 


Fig.  1. 

spectra,  with  complex  double  salts,  with  great  condensation  of  mass,  the 
heavy  metals.  Thus  it  looks  as  if  condensation  of  electronic  orbits 
were  a  maximum  in  these  ferromagnetic  metals  and  that  the  magnetic 
properties  were  related  directly  or  indirectly  to  the  mechanical,  optical 
and  chemical  properties.  It  is  very  remarkable  that  immediately  after 
the  strongly  magnetic  metals  there  follow  the  diamagnetic  metals: 

k 

Cu -0.66 

Ag -1.4 

Tb 

Au -2.6 

On  the  next  diameter  we  have : 

r& 

Zn -0.96 

Cd -1.16 

Ho 

Hg -2.6 

When  we  move  outward  on  a  diameter  of  the  spiral,  the  diamagnetic 


N°L'2VI']  ON  THE  PRESENT  THEORY  OF  MAGNETISM.  J  2  I 

susceptibility  increases.  The  same  rule  is  repeated  by  chlorine,  bromine 
and  iodine;  sulphur,  selenium  and  tellurium;  phosphorus,  arsenic, 
antimony,  bismuth.  If  a  represents  the  atomic  weight,  a  and  j(3  two 
constants,  then  the  atomic  susceptibility  can  be  represented  for  the  last 
three  groups  by 

V"     -  r  +£«-a 

-<rxa  —       -   \^e 

The  same  law  seems  to  hold  for  all  the  groups  of  diamagnetic  elements 
which  are  in  the  previous  representation  on  the  left  of  the  diameter 
passing  through  the  iron  group  and  the  inert  gases.  Thus,  for  instance, 
for  zinc,  cadmium  and  mercury  we  find : 


I.I6-H2.4 
XCA  = g-g io~6  =  15-2  •  io-6, 

2. 6 -2OO 
HO==         13.6  =  38.3-I 

If  we  put 

Xa   =    IO 

we  find  from  Cd  and  Hg  for  a  and  /3  the  values: 
a  =  0.6146,  |8  =  0.00502, 

log  Xzn  =  1.583,  the  calculated  value  =  1.618. 

The  agreement  is  not  so  good  for  the  last  diamagnetic  group  of  elements: 
Cu,  Ag  and  Au,  here  the  atomic  susceptibilities  are  as  follows: 


Xcu  =  5.29 

XAg  =  14.39 -io-6, 

XAn  =  26.55 -io-6. 

The  copper  seems  to  make  an  exception.  Whether  this  is  due  to  an 
inaccurate  determination  of  X  or  to  the  fact  that  this  element  follows 
immediately  after  the  iron  group,  remains  an  open  question.  Between 
the  Zn,  Cd,  Hg  group  and  the  P,  As,  Sb  group  there  are  two  more  groups 
of  diamagnetic  elements,  namely,  those  of  Ga,  -3n>  Tl  and  Ge,  Sn,  Pb. 
The  few  values  of  X  known  for  these  elements  show  that  this  magnetic 
constant  increases  toward  the  periphery  along  the  diamagnetic  diameter 
of  the  spiral. 

If  we  travel  along  the  spiral  from  copper  towards  zinc  and  from  silver 
toward  cadmium,  we  find  the  following  values  for  the  atomic  suscepti- 
bilities. 


122  JAKOB  KUNZ.  [|ER?ES! 

Cu 5.29-10-e  Ag 14.4-10-6 

Zn 8.83  Cd 15.2 

Ga $n 

Ge Sn 5.95 

As 5.8  Sb 77.5 

Se 24.0  Te 38.9 

Br 21.9  3 46.5 

With  the  exceptions  of  As  and  Sn  the  atomic  susceptibility  increases 
from  the  south  toward  the  north  of  the  graphic  representation.  While 
in  the  strongly  magnetic  metals  the  susceptibility  decreases  as  we  move 
on  the  diameter  outward,  the  diamagnetic  susceptibility  increases  when 
we  travel  in  the  same  direction.  Oxygen  occupies  an  exceptional  position 
through  its  paramagnetic  properties.  Its  regular  diamagnetic  properties 
appear  only  in  some  of  the  organic  and  inorganic  compounds. 

No  theory  of  magnetism  is  complete,  which  is  unable  to  account  for 
the  exceptionally  high  magnetic  constants  of  iron,  nickel  and  cobalt 
and  of  the  other  few  ferromagnetic  substances  like  the  Heusler  alloys. 
All  elements  can  be  divided  into  an  electropositive  and  an  electronegative 
group;  all  elements  are  either  para-  or  diamagnetic.  Just  as  we  can  try 
to  ascribe  the  forces  of  affinity  to  electrical  charges  in  the  atom,  we  might 
try  to  reduce  affinity  to  magnetic  forces,  or  magnetons.  It  is  very  inter- 
esting to  note  that  the  strongest  positive  metals  of  the  alkali  group  are 
the  weakest  paramagnetic  elements;  and  that  the  most  negative  elements 
like  F,  Cl,  Br,  !$,  are  rather  strongly  diamagnetic.  While  the  chemical 
properties  of  the  most  electropositive  and  electronegative  elements  may 
be  explained  by  electrical  forces,  it  seems  possible  to  think  that  the  mag- 
netic forces  due  to  magnetic  doublets  play  a  similar  role  in  the  chemical 
affinity  of  the  elements  with  strongly  magnetic  properties.  In  this  way 
we  should  get  a  periodicity  of  the  magnetic  properties  as  functions  of 
the  atomic  weight  as  we  have  a  periodic  variation  of  the  electropositive 
and  negative  properties  of  the  elements.  The  graphical  presentation  of 
the  law  of  periodicity  shows  the  strongly  magnetic  metals  just  opposite 
to  the  strongly  positive  and  negative  metals.  This  explanation  of  the 
periodic  variation  of  the  magnetic  properties  would  obtain  strong  support 
if  it  were  possible  to  prove  that  all  magnetons  are  identical  just  as  all 
electrons  are  identical.  But  there  is  very  little  evidence  in  favor  of  the 
identical  nature  of  all  magnetons  or  elementary  magnets  as  we  shall  see 
in  the  last  paragraph.  In  three  investigations1  published  in  this  journal 
the  moments  of  the  elementary  magnets  and  the  charge  e  have  been 
determined  for  the  following  substances. 

1  The  Absolute  Values  of  the  Moments  of  the  Elementary  Magnets  of  Iron,  Nickel,  and 
Magnetite,  PHYSICAL  REVIEW,  Vol.  XXX.,  p.  359,  1910.  Stifler,  PHYSICAL  REVIEW,  Vol. 
XXXIII. ,  p.  268,  1911.  P.  Gumaer,  PHYSICAL  REVIEW,  Vol.  XXXV.,  p.  288,  1912. 


ON  THE  PRESENT  THEORY  OF  MAGNETISM. 


I23 


WI020 

,-1020 

Fe  

5.15 

1.60 

Fe3O4 

2  02 

0.90 

Ni  

3.65 

1.54 

Co  

6.21 

1.56 

Heusler  alloy  1 

3.55 

1.54 

Heusler  alloy  2  

4.23 

2.04 

1.53- 10-20  =  e  (average). 

This  value  of  e  agrees  fairly  well  with  the  values  obtained  by  independent 
methods.  On  account  of  the  necessary  extrapolations  it  is  difficult  to 
obtain  higher  accuracy. 

While  I  used  the  Langevin-Weiss  theory  for  the  determination  of  the 
elementary  moment  m,  P.  Weiss  himself  measured  the  intensities  of 
magnetization  at  very  low  temperatures,  and  found  noticeable  deviations 
between  the  theory  and  the  experiment  in  the  temperature-intensity 
curve  and  he  found  at  the  same  time  a  common  divisor  among  the  molecu- 
lar intensities  of  the  ferromagnetic  substances.  He  called  that  divisor 
the  magneton-gram,  for  which  he  gave  the  value  1,123.5.  In  addition 
the  paramagnetic  susceptibility  of  Fe3O4  above  the  critical  temperature 
showed  discontinuities  as  function  of  the  temperature,  which  consisted 
of  four  straight  lines,  each  of  which  led  to  a  new  determination  of  the 
magneton.  Finally  P.  Weiss  applied  the  equation 

Cm  =  XmT  =  —— 

to  solutions  of  paramagnetic  substances  containing  iron  and  to  a  con- 
siderable number  of  solid  salts.  It  has  been  shown,  however,  by  Koenigs- 
berger  and  Meslin  that  the  molecular  coefficient  of  magnetization  of  dis- 
solved substances  is  a  function  of  the  concentration;  at  least  for  some 
solutions,  while  for  others  it  seems  to  be  constant.  This  fact  makes  it 
necessary  to  study  solutions  infinitely  dilute  or  undissolved  substances. 
The  number  of  magnetons  found  by  Weiss  in  the  various  sub'stances  is 
shown  by  the  following  series,  in  which  the  values  coincide  nearly  with 
whole  numbers. 

10.41  28.83 

21.89  26.99 

21.96  28.94 

24.04  29.19 

28.03  21.23 

27.93  25.05 

30.09  17.97 

25.99  20.04 

27.11  12.12 

27.91  20.16 

27.69  20.16 


124  JAKOB  KUNZ. 

If  we  displace  the  decimal  point  by  one  cypher  to  the  left,  we  find  again 
approximately  whole  numbers,  which  with  one  exception  are  almost  as 
exact  as  the  numbers  given  by  P.  Weiss.  The  numbers  of  magneton 
per  molecule  is  rather  high  and  it  is  not  very  surprising  that  in  dividing 
for  instance,  32,400  of  FeClsby  1,123.5  one  finds  approximately  a  whole 
number,  28.83  or  2.883  respectively.  The  large  number  of  magnetons 
shown  by  the  last  two  columns  raises  the  question  as  to  why  those 
substances  are  so  weakly  magnetic,  while  nickel,  being  ferromagnetic, 
possesses  at  low  temperatures  only  3  magnetons.  In  addition,  the 
numbers  given  by  P.  Weiss  are  based  on  the  assumption  that  the  magne- 
tization of  the  pure  salts  and  of  the  solutions  varies  according  to  Curie's 
law  down  to  the  absolute  zero.  As  far  as  I  know,  this  assumption  has 
not  yet  been  tested  by  experiments.  Recently  however  Auguste  Piccard1 
measured  with  great  accuracy  the  susceptibility  of  oxygen  at  20°  C. 
and  found  for  the  moment  of  the  atom:  7.8725 .  IO1;  dividing  this  number 
by  1123.4  one  gets  7.007,  a  whole  number  again.  But  in  this  case  H. 
Kamerlingh  Onnes  and  A.  Perrier  have  shown  that  at  low  temperatures 
the  susceptibility  of  oxygen  changes  according  to  the  law: 

2284  _ 


If  this  element  does  not  follow  the  law  of  Curie,  solid  salts  and  solutions 
will  probably  also  show  deviations,  and  at  the  same  time  the  evidence  in 
favor  of  the  magneton  will  decrease.  At  all  events  the  number  of 
magnetons  seems  to  vary  in  the  atom  of  a  given  element  like  nickel,  which 
contains  3  magnetons  at  low  temperature,  8  at  high  temperatures,  9  at 
the  limit  of  the  alloys  of  iron  and  nickel,  16  in  the  solutions.  In  order 
to  determine  the  magneton  P.  Weiss,  abandoning  the  theory,  has  directly 
measured'  the  molecular  moments  of  iron,  nickel  and  cobalt;  Auguste 
Piccard,  on  the  contrary,  has  used  the  theory  in  order  to  find  the  mag- 
neton in  spite  of  the  measurements  of  Kamerlingh  Onnes  and  A.  Perrier. 
If  we  assume  that  Curie's  law  holds  down  to  the  absolute  zero,  we  find 
for  the  elementary  moment  of  oxygen 

m  =  2.58  -io-20. 

The  moment  of  each  individual  magneton  of  Weiss  on  the  other  hand 
would  be  equal  to: 


1  Archives  de  Geneve,  Tome  XXXV.,  p.  480,  1913. 


ON  THE  PRESENT  THEORY  OF  MAGNETISM.  12$ 

If  we  determine  the  molecular  moments  by  means  of  Langevin's  theory, 
we  find  values  varying  from  2.O2-IO"22  to  5.i5*io~20  for  substances  so 
different  among  each  other  as  oxygen,  iron,  magnetite  and  Heusler  alloys. 
These  values  are  of  the  order  of  magnitude  which  we  should  expect  from 
the  theory  of  quanta  by  Planck.  Let  us  assume  that  the  kinetic  energy 
of  a  revolving  electron  %mv2  is  equal  to  a  whole  number  z  times  hn, 
then  we  find  : 

wcoV2  huz 

-  =  zhn  =  -  , 

2  27T 

hz 
cor  =  —  . 

irm 

i 

The  moment  of  M  of  the  revolving  electron  will  be  equal  to  : 

e        e  hz 

M  =  lA  =  irr2-  =  -- 
T 


if  we  put  z  =  i,  we  find  M  =  i.83-io~20;  for  the  frequency  n  we  find 
1.63  •  io15,  assuming  r  =  1.5  •  io~8.  Why  are  these  magnetons  not  sources 
of  light?  Not  much  importance  must  be  attached  to  this  approximate 
.coincidence  of  i.83-io~20  with  the  moments  determined  by  means  of 
Langevin's  theory.  We  find  indeed  about  the  same  magnetic  moment 
without  the  theory  of  the  quanta,  by  calculating  the  velocity  of  the  elec- 
tron by  the  equation  : 

mv2       e2 

—  =  ~2; 

putting  r  =  i.5-io~8;  we  get  n  =  i.4*io15;  M  =  i.54-io~20.  And  the 
question  arises  again,  why  does  such  a  magneton  not  emit  light?  The 
difficulty  might  be  removed  by  admitting  a  large  number  of  electrons 
revolving  in  a  circle,  instead  of  one  electron.  The  assumption  of  one 
single  magneton,  identically  the  same  in  all  substances,  seems  to  require 
much  more  experimental  support,  if  it  exists  at  all. 

LABORATORY  OF  PHYSICS, 

UNIVERSITY  OF  ILLINOIS, 
URBANA,  ILLINOIS, 

February  22,  1915. 


[Reprinted  from  SCIENCE,  N.  S.,  Vol.  XLIL,   A'o. 
1082,  Pages  429-430,  September  24,  1915] 


THE  ABSORPTION  OF  AIR  BY  CHARCOAL  COOLED  TO 
THE  TEMPERATURE  OF  LIQUID  AIR 

THE  remarkable  absorption  of  certain  gases 
by  charcoal  cooled  to  the  temperature  of  liquid 
air,  first  pointed  out  by  Ramsay  and  Soddy, 
may  be  exhibited  conveniently  by  either  of 
two  simple  pieces  of  apparatus.  The  first  (A 
in  the  figure)  makes  use  of  the  electric  dis- 
charge as  an  index  of  the  degree  of  absorption ; 
while  the  second  (B  in  the  figure)  indicates 
the  absorption  by  the  barometric  column  sup- 
ported in  a  vertical  tube  dipping  into  a  bath 
of  mercury. 

The  general  form  and  dimensions  of  the 
discharge-tube  and  its  attached  charcoal  bulb 
are  indicated  in  A.  The  volume  of  the  char- 
coal used  should  be  approximately  equal  to 
that  of  the  discharge  tube  proper.  A  vent 
closed  by  a  valve  is  included.  For  the  experi- 
ment to  be  in  its  best  form  the  cocoanut  char- 
coal should  be  freshly  burned,  and  to  prevent 
undue  absorption  of  air  when  not  in  use  the 
tube  should  be  partially  pumped  out  and  the 
valve  closed.  The  connections  are  made  as 
shown  in  the  figure,  in  which  8  is  an  alterna- 
tive spark  gap  of  about  one  centimeter  length 
in  parallel  with  the  discharge  tube.  Any  in- 
duction coil  about  the  laboratory  will  answer. 
To  operate,  open  the  valve,  then  close  it 
tightly,  thus  allowing  the  pressure  within  the 
tube  to  become  atmospheric.  On  starting  the 
induction  coil  the  spark  will  pass  at  S.  Now 
gently  submerge  the  charcoal  bulb  in  liquid 
air.  In  about  one  minute  the  spark  at  8  will 
begin  to  weaken  and  a  stringy  discharge  will 
appear  between  the  electrodes  of  the  discharge 


To'mBuction 

Ct>.l 


B 


tube.  Soon  the  spark  at  S  will  cease  while  the 
tube  will  be  filled  with  the  characteristic  Geiss- 
ler  tube  glow.  In  about  four  minutes  the 
walls  of  the  discharge  tube  will  begin  to 
flouresce,  due  to  the  bombardment  of  cathode 
rays.  The  intensity  of  this  fluorescence  will 
rapidly  increase  and  soon  the  entire  tube  will 
be  uniformly  filled  with  a  beautiful  apple- 
green  color.  In  about  one  minute  more,  five 
minutes  from  the  start,  the  greenish  color  will 
begin  to  fade  and  sparking  will  reappear  at  8f 
showing  that  the  vacuum  in  the  tube  is  be- 
coming "hard."  In  short  the  pressure  may 
thus  be  reduced  from  atmospheric  to  about 
.001  mm.  mercury  in  five  or  six  minutes  with 
no  other  agency  than  that  of  the  absorption 
of  air  by  charcoal  cooled  to  the  temperature 
of  liquid  air. 

The  second  method  of  showing  the  absorp- 
tion of  air,  due  to  Dr.  L.  T.  Jones,  is  at  once 
clear  by  an  inspection  of  B  in  the  figure. 
The  vertical  stem,  up  to  the  branch  leading  to 
the  charcoal  bulb,  should  be  at  least  78  cm. 


long.  This  stem  may  also  have  an  enlarge- 
ment about  half  way  up  as  shown.  A  valve 
should  be  included  to  protect  the  charcoal 
when  not  in  use.  Before  starting  the  exper- 
iment the  valve  is  opened  and  the  tube 
mounted  in  a  bath  of  mercury.  Liquid  air  is 
then  applied  to  the  charcoal  bulb.  The  ab- 
sorption proceeds  slowly  at  first,  but  soon  gains 
headway  as  the  charcoal  cools.  The  speed  that 
the  mercury  column  acquires  as  it  rises  up 
through  and  fills  the  enlargement  is  surprising. 
Even  with  the  ratio  of  volume  of  tube  to  char- 
coal as  shown  in  the  figure  (approximately 
4 :1)  the  mercury  column  will  mount  to  nearly 
full  atmospheric  pressure  in  the  short  space 
of  five  or  six  minutes. 

Added  interest  is  to  perform  the  two  ex- 
periments simultaneously. 

CHAS.  T.  KNIPP 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
August,  1915 


Acoustics  of  Auditoriums. 

INVESTIGATION  OF  THE  ACOUSTICAL  PROPERTIES  OF  THE  ARMORY 
AT  THE  UNIVERSITY  OF  ILLINOIS. 

By  F.  R.  WATSON,  Associate  Professor  of  Physics,  University  of  Illinois. 

(Reprinted  from  The  Brickbvilder,  October,  1915.) 

THE  Armory  at  the  University  of  Illinois  presents  an  unusual  case  of  defective 
acoustics  because  of  its  very   large  volume   and  comparatively  small  absorbing 
power.     It  was  built  to  fulfil  the  usual  requirements  of  an  armory  in  regard  to 
military  drills  ;  but,  in  addition,  it  has  been  used  on  several  occasions  for  convocations 
and  assemblies  where  the  audiences  have  been  very  large.     The  acoustics  proved  to 
be  impossible  for  speaking  and  music.     In  view  of  the  proposed  continued  use  of  the 
building  for  such  assemblies,   the  writer  carried  on  an  investigation  to  determine  the 
possibilities  of  making  it  satisfactory  in  its  acoustical  properties. 

The  Armory  is  400  feet  long,  212  feet  wide,  and  93  feet  to  the  highest  point  of  the 
roof.     Acoustically,  it  is  defective  because  of  echoes  and  reverberation.     Echoes  are 


Fig.  1.    Framework  of  Parabolic  Reflector 

set  up  by  the  distant  walls,  while  the  reverberation  is  caused  by  the  undue  prolonga- 
tion of  sound. 

Several  experiments  were  tried  to  determine  the  value  of  special  devices  for  reinforc- 
ing and  directing  the  sound.  In  one  case,  a  huge  parabolic  reflector  of  special  con- 
struction was  used.  This  was  based  upon  the  known  action  of  parabolic  reflectors  in 
directing  sound  along  the  axis  of  the  parabola.* 

A  modified  paraboloid  was  constructed,  the  parabolic  ribs  of  which  were  arranged  so 
as  to  spread  the  reflected  sound  over  the  entire  area  occupied  by  the  audience.  The 
framework,  pictured  in  Fig.  1,  was  covered  with  oilcloth  and  mounted  over  the  head 
of  the  speaker  so  that  his  mouth  was  at  the  common  focus  of  all  the  parabolic  ribs. 
Preliminary  tests  with  the  reflector  showed  that  it  admirably  fulfilled  its  purpose  in 


*"  The  Use  of  Sounding  Boards  in  an  Auditorium,"  Physical  Review,  Vol.  1(2),  p.  241,  1913,  and  THE  BRICKBVILDER, 
June,  1913,  and  August,  1913. 


Fig.  3.    Interior  of  Armory 


Fig.  4.    Interior  Arranged  for  Commencement  Exercises 


directing  sound  ;  but  when  used  at  an  assembly  with  an  audience,  its  action  was 
tically  drowned  out  by  the  excessive  reverberation  which  prohibited  any  possibil 
satisfactory  acoustics. 

Another  experiment  of  like  nature  involved  the  use  of  a  special  megaphone  to  di 
ute  the  sound  of  the  speaker's  voice.  This  megaphone  was  more  efficient  ihi 
reflector,  since  it  utilized  all  the  sound  sent  out  by  the  speaker  instead  of  on* 
portion  intercepted  by  the  reflector.  This  device  was  also  of  little  benefit  beca 
the  excessive  reverberation. 

A  third  trial  was  made  by  using  a  number  of  loud-speaking  telephones  at  dif 
positions  in  the  Armory.  This  attempt  was  also  unsuccessful,  although  the  telep 
when  used  out  in  the  open  air  were  very  effective  in  reinforcing  and  directing  the  s 

These  experiments  showed  the  impossibility  of  using  the  entire  Armory  for  spe 
purposes  unless  the  reverberation  could  be  materially  reduced.  The  investigatic 
then  directed  to  the  determination  of  the  constants  of  reverberation  and  the  poss 
of  correcting  them.  Sabine's  method*  was  used  for  this-  purpose.  His  forrm 
reverberation  is  expressed  as  follows  : 


where  t  is  the  time  of  reverberation,  v  the  volume  of  the  room,  a  the  sound-absc 
power  of  all  the  exposed  surfaces  in  the  room,  and  k  a  constant  which  is  deter 
experimentally.  Applying  this  formula  to  the  case  of  the  Armory,  the  volume  of 
is  6,652,000  cubic  feet,  and  the  total  absorbing  power,  without  an  audience, 
units,  the  time  of  reverberation  was  calculated  to  be  24  seconds.  This  value  is  v 
ally  large.  The  Auditorium  at  the  University  of  Illinois,  seating  2,200  people, 
reverberation  before  its  acoustical  correction  of  9  seconds  and  was  considered 
very  bad.f  The  conditions  in  the  Armory  by  comparison  with  this  case  may  be  in 
to  be  exceptionally  unsatisfactory. 

Calculations  made  to  ascertain  the  effect  of  introducing  sound-absorbing  m; 
showed  that  the  installation  of  50,000  square  feet  of  hairfelt  would  reduce  the  reve 
tion  to  4.66  seconds,  a  value  which  would  still  be  too  large  for  satisfactory  spej 
The  only  alternative  was  to  reduce  the  volume.  Calculations  were  then  made  f 
acoustical  properties  of  a  room  partitioned  off  by  canvas  curtains  at  one  end 
Armory  so  as  to  enclose  a  space  212  feet  by  134  feet  and  35  feet  high.  To  do  1 
was  first  necessary  to  determine  experimentally  the  action  of  the  canvas  in  transn 
and  absorbing  sound.  The  time  of  reverberation  for  the  room  with  an  audie 
4,500  people  present  was  then  estimated  to  be  1.1  seconds,  a  value  which  ha; 
found  by  repeated  experience  to  be  satisfactory. 

On  the  basis  of  this  calculation  a  room  of  the  specified  dimensions  was  enclo 
one  end  of  the  Armory  and  used  for  the  University  Commencement  exercises. 
Fig.  4.)     Auditors  in  all  parts  of  this  canvas-enclosed  room  could  hear  and  unde: 
the  various  speakers,  so  that  the  room  was  considered  a  success  from  the  standp< 
acoustics. 

A  further  step  to  be  undertaken  in  the  investigation  lies  in  the  proposed  instal 
of  some  sound-absorbing  materials  upon  the  walls  of  the  Armory  itself.     It  is 
that  by  this  means  the  time  of  reverberation  may  be  reduced  to  a  reasonable  leng 
make  the  building  entirely  satisfactory  for  military  drills  and  band  concerts.     Wl 
or  not  it  will  also  be  suitable  for  assemblies  where  there  is  speaking,  remains  to  be 


[Reprinted  from  the  PHYSICAL  REIVEW,  N.S.,  Vol.  VI.  No.  5,  November,  1915.] 


SATURATION  VALUE  OF  THE  INTENSITY  OF  MAGNETIZA- 
TION AND  THE  THEORY  OF  THE  HYSTERESIS  LOOP. 

BY  E.  H.  WILLIAMS. 

T3  ECENTLY,  Weiss1  has  shown  that  an  alloy  composed  of  iron  and 
V\  cobalt  combined  in  relative  amounts  given  by  the  expression 
Fe2Co  gives  a  much  higher  value  of  the  intensity  of  magnetization  than 
either  iron  or  cobalt  taken  alone.  Furthermore,  it  has  been  shown  by 
Mr.  D.  T.  Yensen2  that  the  magnetic  properties  of  pure  iron  can  be 
greatly  improved  by  melting  the  iron  in  a  vacuum  and  it  was  hoped  that 
the  magnetic  properties  of  Fe2Co  could  be  improved  by  treating  it  in 
like  manner.  The  object  of  the  present  paper  was  not  only  to  make  a 
careful  study  of  the  saturation  value  of  the  intensity  of  magnetization 
of  Fe2Co  prepared  under  various  conditions  but  to  use  the  data  thus 
obtained  in  a  test  of  the  theory  of  the  hysteresis  loop  as  developed  by 
J.  Kunz.3 

In  his  paper,  Kunz  tests  the  theory  with  the  data  then  available. 
The  results  show  the  discrepancy  between  theory  and  experiment  to  be 
very  great.  If  all  quantities  involved  are  obtained  from  the  same 
sample,  the  test  of  the  theory  will  be  more  satisfactory. 

PREPARATION  OF  SAMPLES. 

Iron  and  cobalt  were  taken  in  the  proportion  indicated  by  the  formula 
Fe2Co,  melted  in  a  vacuum  furnace  under  pressures  varying  from  5  mm. 
to  0.5  mm.  Hg,  allowed  to  cool  slowly  and  then  forged  into  long  bars 
from  which  samples  were  turned.  In  most  cases  enough  of  the  material 
was  taken  to  make  both  an  ellipsoid  and  a  rod — the  ellipsoid  for  the 
determination  of  the  saturation  value  of  the  intensity  of  magnetization 
and  the  rod  for  the  determination  of  the  hysteresis  loop.  The  hysteresis 
data  were  taken  by  Mr.  D.  T.  Yensen  on  a  magnetic  testing  apparatus 
similar  to  those  used  by  the  Bureau  of  Standards.  Mr.  Yensen  has  made 
a  study  of  the  samples  from  the  viewpoint  of  the  engineer.  His  results 
are  to  be  published  soon  in  the  General  Electric  Review. 

1  P.  Weiss,  Compt.  Rend.,  156,  p.  1970,  1913. 

!D.  T.  Yensen,  Bui.  No.  72,  Eng.  Exp.  Sta.,  Univ.  of  Illinois,  Urbana,  111. 
;J.  Kunz,  Phys.  Zeit.,  XIII. ,  p.  591,  1912. 


directing  sound  ;  but  when  used  at  an  assembly  with  an  audience,  its  action  was  prac- 
tically drowned  out  by  the  excessive  reverberation  which  prohibited  any  possibility  of 
satisfactory  acoustics. 

Another  experiment  of  like  nature  involved  the  use  of  a  special  megaphone  to  distrib- 
ute the  sound  of  the  speaker's  voice.  This  megaphone  was  more  efficient  than  the 
reflector,  since  it  utilized  all  the  sound  sent  out  by  the  speaker  instead  of  only  the 
portion  intercepted  by  the  reflector.  This  device  was  also  of  little  benefit  because  of 
the  excessive  reverberation. 

A  third  trial  was  made  by  using  a  number  of  loud-speaking  telephones  at  different 
positions  in  the  Armory.  This  attempt  was  also  unsuccessful,  although  the  telephones 
when  used  out  in  the  open  air  were  very  effective  in  reinforcing  and  directing  the  sound. 

These  experiments  showed  the  impossibility  of  using  the  entire  Armory  for  speaking 
purposes  unless  the  reverberation  could  be  materially  reduced.  The  investigation  was 
then  directed  to  the  determination  of  the  constants  of  reverberation  and  the  possibility 
of  correcting  them.  Sabine's  method*  was  used  for  this-  purpose.  His  formula  for 
reverberation  is  expressed  as  follows  : 


where  t  is  the  time  of  reverberation,  v  the  volume  of  the  room,  a  the  sound-absorbing 
power  of  all  the  exposed  surfaces  in  the  room,  and  k  a  constant  which  is  determined 
experimentally.  Applying  this  formula  to  the  case  of  the  Armory,  the  volume  of  which 
is  6,652,000  cubic  feet,  and  the  total  absorbing  power,  without  an  audience,  13,400 
units,  the  time  of  reverberation  was  calculated  to  be  24  seconds.  This  value  is  unusu- 
ally large.  The  Auditorium  at  the  University  of  Illinois,  seating  2,200  people,  had  a 
reverberation  before  its  acoustical  correction  of  9  seconds  and  was  considered  to  be 
very  bad.f  The  conditions  in  the  Armory  by  comparison  with  this  case  may  be  inferred 
to  be  exceptionally  unsatisfactory. 

Calculations  made  to  ascertain  the  effect  of  introducing  sound-absorbing  material 
showed  that  the  installation  of  50,000  square  feet  of  hairfelt  would  reduce  the  reverbera- 
tion to  4.66  seconds,  a  value  which  would  still  be  too  large  for  satisfactory  speaking. 
The  only  alternative  was  to  reduce  the  volume.  Calculations  were  then  made  for  the 
acoustical  properties  of  a  room  partitioned  off  by  canvas  curtains  at  one  end  of  the 
Armory  so  as  to  enclose  a  space  212  feet  by  134  feet  and  35  feet  high.  To  do  this  it 
was  first  necessary  to  determine  experimentally  the  action  of  the  canvas  in  transmitting 
and  absorbing  sound.  The  time  of  reverberation  for  the  room  with  an  audience  of 
4,500  people  present  was  then  estimated  to  be  1.1  seconds,  a  value  which  has  been 
found  by  repeated  experience  to  be  satisfactory. 

On  the  basis  of  this  calculation  a  room  of  the  specified  dimensions  was  enclosed  at 
one  end  of  the  Armory  and  used  for  the  University  Commencement  exercises.  (See 
Fig.  4.)  Auditors  in  all  parts  of  this  canvas-enclosed  room  could  hear  and  understand 
the  various  speakers,  so  that  the  room  was  considered  a  success  from  the  standpoint  of 
acoustics. 

A  further  step  to  be  undertaken  in  the  investigation  lies  in  the  proposed  installation 
of  some  sound-absorbing  materials  upon  the  walls  of  the  Armory  itself.  It  is  hoped 
that  by  this  means  the  time  of  reverberation  may  be  reduced  to  a  reasonable  length  and 
make  the  building  entirely  satisfactory  for  military  drills  and  band  concerts.  Whether 
or  not  it  will  also  be  suitable  for  assemblies  where  there  is  speaking,  remains  to  be  seen. 


*  American  Architect,  1900. 

t"  Acoustics  of  Auditoriums,"  Bulletin  No.  73  of  the  University  of  Illinois,  Engineering  Experiment  Station. 


[Reprinted  from  the  PHYSICAL  REIVEW,  N.S.,  Vol.  VI.  No.  5,  November,  1915.] 


SATURATION  VALUE  OF  THE  INTENSITY  OF  MAGNETIZA- 
TION AND  THE  THEORY  OF  THE  HYSTERESIS  LOOP. 

BY  E.  H.  WILLIAMS. 

ECENTLY,  Weiss1  has  shown  that  an  alloy  composed  of  iron  and 
cobalt  combined  in  relative  amounts  given  by  the  expression 
Fe2Co  gives  a  much  higher  value  of  the  intensity  of  magnetization  than 
either  iron  or  cobalt  taken  alone.  Furthermore,  it  has  been  shown  by 
Mr.  D.  T.  Yensen2  that  the  magnetic  properties  of  pure  iron  can  be 
greatly  improved  by  melting  the  iron  in  a  vacuum  and  it  was  hoped  that 
the  magnetic  properties  of  Fe2Co  could  be  improved  by  treating  it  in 
like  manner.  The  object  of  the  present  paper  was  not  only  to  make  a 
careful  study  of  the  saturation  value  of  the  intensity  of  magnetization 
of  Fe2Co  prepared  under  various  conditions  but  to  use  the  data  thus 
obtained  in  a  test  of  the  theory  of  the  hysteresis  loop  as  developed  by 
J.  Kunz.3 

In  his  paper,  Kunz  tests  the  theory  with  the  data  then  available. 
The  results  show  the  discrepancy  between  theory  and  experiment  to  be 
very  great.  If  all  quantities  involved  are  obtained  from  the  same 
sample,  the  test  of  the  theory  will  be  more  satisfactory. 

PREPARATION  OF  SAMPLES. 

Iron  and  cobalt  were  taken  in  the  proportion  indicated  by  the  formula 
Fe2Co,  melted  in  a  vacuum  furnace  under  pressures  varying  from  5  mm. 
to  0.5  mm.  Hg,  allowed  to  cool  slowly  and  then  forged  into  long  bars 
from  which  samples  were  turned.  In  most  cases  enough  of  the  material 
was  taken  to  make  both  an  ellipsoid  and  a  rod — the  ellipsoid  for  the 
determination  of  the  saturation  value  of  the  intensity  of  magnetization 
and  the  rod  for  the  determination  of  the  hysteresis  loop.  The  hysteresis 
data  were  taken  by  Mr.  D.  T.  Yensen  on  a  magnetic  testing  apparatus 
similar  to  those  used  by  the  Bureau  of  Standards.  Mr.  Yensen  has  made 
a  study  of  the  samples  from  the  viewpoint  of  the  engineer.  His  results 
are  to  be  published  soon  in  the  General  Electric  Review. 

1  P.  Weiss,  Compt.  Rend.,  156,  p.  1970,  1913. 

5D.  T.  Yensen,  Bui.  No.  72,  Eng.  Exp.  Sta.,  Univ.  of  Illinois,  Urbana,  111. 
5J.  Kunz,  Phys.  Zeit.,  XIII. ,  p.  591,  1912. 


405  E.    H.    WILLIAMS. 

ELLIPSOIDS. 

A  great  deal  of  trouble  was  experienced  in  making  ellipsoids  that  were 
accurate.  The  form  of  the  ellipsoids  was  tested  by  projecting  an  image 
of  the  ellipsoid  on  the  figure  of  an  ellipsoid  drawn  to  the  desired  pro- 
portions. Finally  the  accuracy  was  tested  by  comparing  the  volumes 
obtained  by  calculation,  using  the  dimensions  of  the  ellipsoid,  with  those 
obtained  by  immersion  in  distilled  water  at  known  temperature.  No 
ellipsoid  was  used  where  the  difference  in  volume  differed  by  more  than 
2  per  cent,  and  most  of  them  differed  by  less  than  I  per  cent.  The  ellip- 
soids were  about  1.19  cm.  in  length  and  about  .56  cm.  in  diameter. 

The  author  wishes  to  express  his  thanks  to  P.  Weiss  for  samples  of 
his  material  which  he  kindly  sent.  This  material,  when  received,  was 
porous  and  had  apparently  been  melted  and  cast  at  atmospheric  pressure. 
One  ellipsoid  was  turned  from  the  material  just  as  received.  A  second 
ellipsoid  was  turned  from  a  portion  of  the  material  which  had  been  forged 
into  a  small  rod,  after  which  the  remainder  of  the  sample  was  remelted 
in  a  vacuum  furnace  under  a  pressure  of  .5  mm.  of  Hg.  It  was  then 
forged  into  a  rod  from  which  an  ellipsoid  was  turned.  The  results 
obtained  with  these  ellipsoids  are  included  in  Table  I. 

The  field  inside  an  ellipsoid  is  uniform  and  is  given  by 

H  =  Ho  -  NIt  (i) 

where  H0  is  the  external  field  applied,  /  the  intensity  of  magnetization, 
H  the  resultant  field  within  the  ellipsoid  and  N  a  constant  depending  on 
the  dimensions  of  the  ellipsoid. 

The  field  HQ  was  produced  by  a  large  electromagnet  the  pole  pieces 
of  which  were  3.2  cm.  apart  and  bored  to  receive  a  glass  tube  9  mm.  in 
diameter.  On  this  tube  was  wound  an  induction  helix.  The  field,  H0, 
between  the  poles  of  the  magnet  was  calibrated  by  two  methods — by 
means  of  a  flip  coil  and  with  a  magnetic  balance.  The  mean  of  the 
two  calibrations,  which  differed  in  no  case  by  more  than  one  half  of  one 
per  cent.,  was  taken  to  plot  the  calibration  curve.  The  intensity  of 
magnetization  /  was  obtained  by  suddenly  removing  the  ellipsoid  from 
the  induction  helix  between  the  pole  pieces  and  noting  the  change  of 
flux  as  indicated  by  a  ballistic  galvanometer.  From  the  constants  of  the 
apparatus  the  value  of  I  could  be  calculated. 

If,  in  equation  (i),  NI  is  greater  than  H0,  H  becomes  negative  while 
HQ  and  I  are  still  positive,  i.  e.,  the  field  within  the  ellipsoid  is  opposite 
in  direction  to  the  field  outside.  The  ellipsoids  used  in  this  work  were 
such  as  to  produce  this  result,  so  that  when  a  hysteresis  loop  was  taken 
with  one  of  the  ellipsoids  a  very  peculiar  S-shaped  form  was  obtained. 


INTENSITY   OF   MAGNETIZATION.  406 

RESULTS  FOR  Im. 

The  results  for  the  saturation  values  of  the  intensity  of  magnetization 
are  summarized  in  Table  I.  In  this  table  also,  values  obtained  by  other 
experimenters  as  well  as  by  the  author  are  given  for  comparison.  An- 
nealing these  samples  at  900°  C.  and  1100°  C.  produced  practically  no 
change  in  the  values  of  Im.  Analysis  of  the  first  two  samples  of  Fe2Co 
listed  in  Table  I.,  were  made,  the  first  showing  33.36  per  cent.  Co  and 
the  second  33.33  per  cent.  Co.  From  these  results  we  see  that  com- 

TABLE  I. 

Values  of  Im     (t  =  20°  C.) 

Commercial  steel  (Williams) 1,751 

Swedish  wrought  iron  (Ewing) .1,690 

Bessemer  steel  (.4  per  cent.  C.) 1,770 

Electrolytic  iron  (melted  under  pressure  of  3  mm.  of  Hg 

(Williams) 1,798 

Cobalt  (1.66  per  cent.  Fe)  (Ewing) 1,310 

Cobalt  (pure)  (Stifler) 1,421 

Cobalt  (melted  under  pressure  of  1  mm.  Hg  (about  99  per 

cent,  pure)  (Williams) 1,504 

Fe2Co  melted  under  pressure  of  3  mm.  of  Hg  without  being 

forged  (Williams) 1,791 

Same — hand  forged  (Williams) 1,962 

Same — forged  with  steam  hammer  (Williams) 1,977 

Fe2Co  melted  under  pressure  of  1  mm.  of  Hg.     Forged  with 

steam  hammer  (Williams) 2,050 

Fe2Co  melted  under  pressure  of  0.5  mm.  of  Hg.     Forged 

with  steam  hammer  (Williams) 2,056 

Fe2Co  melted  and  cast  at  atmospheric  pressure  (sample  re- 
ceived from  P.  Weiss)   (Williams) 1,752 

Same — forged  as  received  (Williams) 1,977 

Same — remelted  under  .5  mm.  pressure  and  forged  (Williams).  .2,038 

bining  pure  iron  for  which  the  value  of  Im  is  1,800,  when  the  iron  is 
melted  in  a  vacuum,  with  cobalt  for  which  the  value  of  Im  is  1,500  when 
melted  under  the  same  conditions,  we  obtain  an  alloy  for  which  Im  is 
2,050,  or  14  per  cent,  higher  than  pure  iron  itself.  Weiss,  in  the  paper 
referred  to  above,  states  that  if  one  takes  into  account  the  difference  in 
atomic  weight,  the  temperature  at  which  ferromagnetism  disappears 
and  the  densities,  one  finds  that  at  ordinary  temperatures  ferro-cobalt 
has  a  magnetization  at  saturation  10  per  cent,  higher  than  that  of  iron, 
so  that  the  extra  4  per  cent,  is  probably  due  to  the  fact  that  the  alloy 
in  the  present  case  was  melted  in  a  vacuum.  This  conclusion  is  sub- 


407 


E.   H.    WILLIAMS. 


[SECOND 

[SERIES. 


stantiated  by  the  difference  between  the  last  two  results  of  Table  I. 
(material  received  from  P.  Weiss).  This  difference  is  undoubtedly  due 
to  melting  under  greatly  reduced  pressure  since  all  other  conditions  are 
as  nearly  equal  as  it  was  possible  to  make  them. 

Photomicrographs  of  the  first  two  samples  of  Fe2Co  given  in  Table  I. 
are  shown  in  Figs.  I,  2,  3  and  4.  Fig.  I  is  of  the  first  sample  after  being 
forged  and  Fig.  2  is  of  the  same  sample  after  being  annealed  at  900°  C. 
and  cooled  uniformly  at  the  rate  of  30°  C.  per  hour.  Fig.  3  is  of  the 
second  sample  of  Fe2Co  listed  in  Table  I.  after  the  same  had  been  forged 
and  Fig.  4  is  the  same  sample  after  being  annealed  at  900°  C. 

HYSTERESIS  THEORY. 

In  the  article  by  J.  Kunz  referred  to  above,  the  author  obtains  the 
following  expression  for  the  energy  of  the  hysteresis  loop: 


W  = 


'i  +  A/! 


I                               I 

rr  2 

/„                    (Hi  -  Atf)2 

I* 

+   /I    +   A/! 

where  Im  is  the  saturation  value  of  the  intensity  of  magnetization,  He 
the  coercive  force,  /i  the  intensity  of  magnetization  corresponding  to 
the  magnetizing  field  HI,  and  where 


and 


According  to  this  theory  the  hysteresis  loss  per  cycle  experienced 
when  the  field  alternates  between  the  values  +  HI  and  —  HI,  producing 
the  intensities  of  magnetization  +  I\  and  —  /i,  can  be  calculated  directly 
if  one  knows  the  values  of  Im  and  Hc  for  the  material  concerned. 

As  pointed  out  above,  the  test  given  this  theory  proved  very  unsatis- 
factory and  seemed  to  indicate  that  the  theory  was  of  very  little  practical 
importance. 

It  seemed  desirable  to  give  the  theory  a  thorough  test  by  the  careful 
determination  of  the  four  quantities  Im,  Hc,  HI  and  I\  with  the  same 
sample.  The  results  for  the  hysteresis  loss,  W,  calculated  and  the 
hysteresis  loss,  W,  as  measured  from  the  hysteresis  loops  are  given  in 


PHYSICAL  REVIEW,  VOL.  VI.,  SECOND  SERIES. 
November,  1915. 


PLATE  I. 
To  face  page  408. 


Fig.  1. 

FezCo   melted    under   3    mm.    pressure  and 
forged. 


Fig.  2. 
Same  as  Fig.  i,  annealed  at  900°  C. 


Fig.  3. 

Fe2Co   melted   under   i    mm.    pressure   and 
forged. 


Fig.  4. 
Same  as  Fig.  3,  annealed  at  900°  C. 


E.   H.  WILLIAMS. 


VOL.  VI.l 
No.  5.     J 


INTENSITY   OF   MAGNETIZATION. 


408 


Tables  II.,  III.  and  IV.     Table  II.  is  for  a  sample  of  Fe2Co  before  being 
annealed;  Table  III.  for  the  same  sample  after  being  annealed  at  900°  C., 


ust eres/s   Curves 
•for     Fe^Co     after 
Anneahna     at     <J000C 


and  Table  IV.  for  a  sample  of  pure  iron  after  being  annealed  at  900°  C. 
The  hysteresis  curves  from  which  the  values  of  W  in  Table  III.  were 
measured  are  shown  in  Fig.  5. 

TABLE  II. 

Im  =  2,050;     Hc  =  6.4;     AH  =  1.876. 


HI 

/i 

A/i 

w 

W 

14 

415 

143.5 

19,580 

18,685 

24.5 

798 

24.2 

28,700 

28,600 

56.5 

1,179 

2.27 

35,620 

41,825 

146. 

1,588 

.06 

45,630 

56,245 

The  results  in  Tables  II.,  III.  and  IV.  show  fairly  good  agreement 
between  the  values  for  the  hysteresis  loss  as  calculated  by  the  above 
formula  and  those  obtained  by  measurement  of  the  hysteresis  curves. 

If  the  theory  were  modified  to  take  into  account  the  curvature  as  the 


409 


E.   H.    WILLIAMS. 

TABLE  III. 

Im  =  2,050;     Hc  =  0.65;     AH  =  0.19. 


[SECOND 

[SERIES. 


ffl 

/i 

A/i 

w 

w 

.95 

796 

537. 

1,513 

1,488 

1.82 

955 

64.4 

2,727 

2,340 

3.82 

1,115 

6.35 

3,434 

3,020 

7.33 

1,273 

.902 

3,777 

3,792 

29. 

1,590 

.013 

4,166 

4,930 

TABLE  IV. 

1,800;     Hc  =  0.36;     AH  =  0.105. 


Hi 

/i 

A/i 

w 

W 

.6 

955 

306. 

973 

970 

0.9 

1,115 

81. 

1,364 

1,353 

1.5 

1,195 

16. 

1,651 

1,552 

6.5 

1,264 

.2 

1,940 

1,918 

coercive  force  is  being  applied,  it  would  probably  agree  with  experiment 
even  more  accurately  than  it  now  does.  But  even  as  it  stands  the 
results  for  ordinary  fields  are  accurate  enough  to  make  the  theory  of 
great  value  in  calculating  losses  where  they  cannot  be  measured  directly. 

PHYSICS  DEPARTMENT, 

UNIVERSITY  OF  ILLINOIS, 
May,  1915. 


[Reprinted  from  SCIENCE,  N.  S.,  Vol.  XLIL,   No. 
1096,  Pages  942-94S,  December  Si,  1915] 


COLOR  EFFECTS  OF  POSITIVE  AND  OF  CATHODE  RAYS 
IN  RESIDUAL  AIR,   HYDROGEN,  HELIUM,  ETC. 

As  is  well  known  positive  rays  have  their 
origin  in  front  of  the  cathode,  and  under  the 
action  of  the  electric  force  fall  toward  it.  If 
the  cathode  is  perforated  the  rays  stream 
through  and  constitute  the  "kanal  strahlen" 
of  Goldstein.  Tubes  built  to  exhibit  this  phe- 
nomenon form  a  part  of  the  regular  equip- 
ment of  nearly  all  collections  of  apparatus  in- 
tended to  exhibit  the  phenomena  of  electric 
discharge  through  gases. 

Most  beautiful  and  striking  color  effects 
may  be  had  by  using  hollow  cathodes1  in 
specially  designed  tubes  containing  each  a 
trace  of  some  inert  gas  such  as  helium,  argon 
or  neon.  The  color  effect  is  striking  because 
the  cathode  beam  is  of  one  color,  while  the 
positive  ray  beam  in  the  same  gas  is  of  an  en- 
tirely different  color.  The  general  design  of 
the  tubes  that  Dr.  Jakob  Kunz  and  the  writer 
have  found  best  suited  is  shown  in  the  accom- 
panying figure.  The  discharge  tube  is  dumb- 
bell shaped.  It  is  made  of  two  2  liter  Florence 
flasks,  M  and  N.  The  hollow  cylindrical 
cathode  C  is  mounted  in  the  neck,  while  the 
anode  A  is  placed  in  one  of  the  bulbs.  The 
cathode  terminal  C,  the  nipple  p  for  exhaust- 
ing, and  the  charcoal  bulb  B  are  all  attached 
to  one  vertical  tube  as  shown. 

The  process  of  filling  the  discharge  tube, 
sealing  it  off  from  the  pump,  and  its  subse- 
quent use  is  as  follows :  After  the  tube  is  con- 

i  J.  J.  Thomson,  "Rays  of  Positive  Electricity/' 
p.  6,  1913. 


structed,  and  the  charcoal  bulb  B  attached, 
the  exhaust  nipple  is  put  in  communication 
with  a  pump,  and  also  to  some  source  of  the 
gas  to  be  used.  During  the  early  part  of  the 
exhaustion  it  is  well  to  gently  heat  the  bulb  B. 
Continue  the  pumping  until  the  tube  on 
sparking  shows  a  tendency  of  becoming  hard. 


As  this  stage  is  approached  cathode  rays  will 
appear  as  a  compact  beam  in  the  bulb  N, 
while  a  beam  of  positive  rays  will  traverse  the 
bulb  M .  Now  admit  a  small  quantity  of  the 
desired  gas,  say,  helium.  The  chances  are  that 
too  much  gas  will  enter  the  discharge  tube  and 
thus  destroy  the  definition  of  the  two  beams. 
To  restore  it  pumping  should  be  continued 
and  at  the  same  time  the  bulb  B  should  be 
carefully  submerged  in  liquid  air.  Care  must 
be  exercised  not  to  reduce  the  content  of 
helium  by  too  long  continued  pumping.  The 
cooled  charcoal  will  absorb  the  traces  of  air 
leaving  the  tube  MN  relatively  richer  and 
richer  in  helium — since  helium,  an  inert  gas, 
is  but  slightly  absorbed  by  the  cooled  charcoal. 
The  cathode  beam  in  N  as  well  as  the  positive 
ray  beam  in  M  will  each  increase  in  bright- 


ness  and  definition,  reaching  a  maximum, 
after  which,  as  the  process  continues,  they  will 
begin  to  fade.  At  the  stage  when  the  beams 
are  judged  brightest  the  exhaust  nipple  p  is 
sealed  off  from  the  pump.  The  tube  is  now  in 
its  finished  state.  Removing  the  liquid  air, 
the  charcoal  gives  up  its  absorbed  gas  and  the 
beams  weaken  and  become  diffused.  For  sub- 
sequent use  it  is  only  necessary  to  submerge 
B  in  liquid  air  while  the  discharge  from  an 
induction  coil  is  passing.  The  beams  in  M 
and  N  will  increase  in  brightness  and  defini- 
tion as  the  absorption  of  the  active  gases  pro- 
ceeds, thus  giving  ample  time  for  the  observa- 
tion of  the  changes  going  on  within  the  tube. 

The  most  interesting  phenomenon  is  the 
color  of  the  two  beams.  The  cathode  beam  in 
helium  is  a  greenish  gray  color,  while  the  posi- 
tive ray  beam  in  the  same  gas  is  a  beautiful 
red.  There  is  no  mistaking  the  colors.  In- 
deed the  red  due  to  the  positive  ions  is  so  per- 
sistent that  it  appears  at  the  very  origin  of 
these  rays — at  the  edge  of  the  Crookes  dark 
space  in  front  of  the  cathode  (shown  by  the 
dotted  line  mn  in  the  figure). 

The  usefulness  of  the  above  described  tube 
for  many  laboratories  is  limited  because  liquid 
air  is  used  in  its  initial  adjustment  and  sub- 
sequent operation.  If  desired  the  bulb  B  may 
also  be  sealed  off.  The  only  disadvantage  is 
that  this  fixes  the  gas  content  in  the  tube.  In 
case  no  liquid  air  is  available  it  is  still  possi- 
ble to  construct  the  tube  provided  access  may 
be  had  to  a  good  pump.  In  this  event  the  dis- 
charge tube  should  be  washed  out  several  times 
with  the  desired  gas,  in  order  to  remove  every 
trace  of  air,  and  then  sealed  off  when  the 
beams  are  brightest.  This  gives  a  permanent 
tube  provided  the  occluded  gases  in  the  elec- 
trodes and  walls  of  the  vessel  do  not  in  time 
let  the  vacuum  down.  Danger  from  this 
source,  however,  may  be  largely  avoided  by 
gently  heating  the  tube  during  exhaustion. 


The  obvious  advantage  of  a  charcoal  bulb  is 
that  the  proper  exhaustion  can  always  be 
reached  and  at  the  same  time  the  discharge  at 
various  stages  of  exhaustion  successively  ex- 
hibited. 

It  should  be  added  that  the  best  results  only 
are  obtained  when  the  hollow  cathode  C,  which 
is  an  aluminum  cylinder  closed  at  the  ends 
with  aluminum  discs  through  the  center  of 
each  is  cut  a  rectangular  opening  about  1  mm. 
by  6  mm.,  is  placed  exactly  on  the  axis  of  the 
tube  connecting  the  bulbs  M  and  N.  The  cor- 
rect position  is  shown  in  the  figure,  end  view 
at  6,  and  side  view  at  d.  The  discharge  leav- 
ing the  cathode,  confined  in  a  narrow  tube  as 
here,  is  always  along  the  axis  of  the  glass 
tube,  regardless  of  the  alignment  of  the  cath- 
ode. In  other  words,  the  shape  of  the  glass 
tube  rather  than  the  shape  of  the  cathode 
determines  the  position  of  the  cathode  beam- 
Lack  of  alignment  is  shown  at  c  and  e  where 
the  opening  through  the  hollow  cathode  is 
below  the  axis  and  as  a  result  few  positive  rays 
get  through  and  show  in  the  bulb  M9  though 
they  show  distinctly  at  their  origin  in  front  of 
the  cathode.  To  avoid  possible  lack  of  align- 
ment it  is  advised  to  make  the  hollow  cathode 
C  of  such  diameter  so  as  to  fit  snugly  into  the 
neck  connecting  M  and  N  as  shown  in  a  of  the 
figure. 

An  interesting  test  to  show  that  the  beam  in 
N  is  composed  of  electrons,  and  that  in  M  of 
positively  charged  ions,  is  to  deflect  them  in 
turn  by  a  strong  electro-magnet.  The  cathode 
beam  is  readily  deflected  while  the  positive 
ray  beam  is  but  little  deflected  and  that  in  the 
opposite  sense.  This  is  in  full  agreement  with 
the  theory  of  the  magnetic  deflection  of  mov- 
ing positive  and  negative  charges. 

CHAS.  T.  KNIPP 
LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
October  9,  1915 


[Reprinted  from  the  PHYSICAL  REIVEW,  N.S.,  Vol.  VI.  No.  6,  December,  1915.] 


THE  STRUCTURE  OF  7  RAYS  ON  THE  BASIS  OF  THE 
ELECTRO-MAGNETIC  THEORY  OF  LIGHT. 

BY  JAKOB  KUNZ. 

THE  difficulties  in  the  theories  of  radiation  have  become  so  great  in 
the  last  few  years  that  only  a  very  fundamental  new  idea  will  be 
able  to  bring  harmony  into  the  present  chaos  of  facts  and  theories. 
Before  that  solving  idea  appears,  we  can  only  draw  all  the  logical  con- 
clusions which  follow  from  a  given  hypothesis  and  compare  these  con- 
clusions with  experiments.  This  procedure  leads  to  the  result  that 
neither  one  of  the  present  hypotheses  is  able  to  coordinate  satisfactorily 
all  the  facts.  The  electromagnetic  undulatory  theory  of  light  explains 
the  phenomena  of  reflection,  refraction,  interference,  diffraction,  etc., 
but  it  fails  to  explain  the  phenomena  of  radiation,  the  photoelectric  and 
the  related  effects.  The  corpuscular  theories  and  the  quantum  theories- 
on  the  other  hand  are  especially  invented  for  the  explanation  of  the  latter 
group  of  phenomena,  failing  to  account  for  the  first  group.  Not  only 
are  the  fundamental  assumptions  of  the  two  theories  different,  but  the 
older  electromagnetic  undulatory  theory  gives  not  only  mathematical 
relations  between  the  different  quantities  involved,  but  it  visualizes  at 
the  same  time,  the  phenomena,  which  are  explained,  so  that  we  can  see 
the  mechanism  of  the  processes.  The  recent  quantum  theories  on  the 
other  hand  give  us  only  algebraic  relations  between  different  quantities 
such  as  the  law  of  the  photoelectric  effect  %mv2  =  hn  —  Vo,  without  giving 
us  the  least  idea  as  to  the  mechanism  of  the  phenomenon.  It  seems  to  be 
advantageous  if  not  necessary  for  a  theory  to  visualize  the  phenomena. 
Led  by  this  idea,  I  shall  show  by  the  following  figures  and  calculations 
that  the  electromagnetic  theory  of  very  hard  Roentgen  and  7  rays  leads 
to  conclusions  which  remind  us  of  an  emission  or  corpuscular  theory  of 
rays.  The  problem  has  already  been  solved  by  A.  Sommerfeld,1  "Uber 

1  Sitzungsberichte  der  K.  B.  Akademie  der  Wissenschaften,  41,  p.  i,  1911. 

413 


414 


JAKOB  KUNZ. 


[SECOND 

[SERIES. 


die  Structur  der  7  Strahlen."  I  shall  use,  however,  a  different  method 
which  allows  the  visualizing  of  the  remarkable  conclusion  of  the  electro- 
magnetic theory. 

An  electron  moves  with  the  velocity  v  in  the  x  direction;  the  electric 
force  E  at  a  distance  r  from  the  charge  making  an  angle  p  with  the 
direction  of  motion  is  equal  to 


E  = 


x,  y,  z  are  the  coordinates  of  the  point  in  which  the  electric  force  E  is 
measured,  the  zero  of  the  system  of  the  coordinates  lies  in  the  electron. 
We  can  express  E  also  in  the  following  way 


E  = 


e  \  i 


The  magnetic  force  H  is  given  by 


H  = 


Ev  sin  <p 


These  equations  tell  us  that  with  increasing  velocity  v  the  electromagnetic 

field  following  the  electron,  is  more  and  more 
compressed  as  it  were  toward  the  equatorial 
plane,  being  perpendicular  to  the  direction 
of  motion. 

If  now  the  electron  comes  into  collision 
with  a  metallic  plate  it  will  come  to  rest  dur- 
ing an  interval  of  time  t  and  move  mean- 
while over  the  distance  /.  If  we  draw  the 
line  of  force  t  seconds  after  the  collision  be- 
gan, we  find  the  well-known  disturbance 
within  the  Roentgen  pulse,  whose  thickness 


Fig.  1. 


d  is  a  function  of  &  given  by  the  equation 

d  =  -  (20  —  v  cos  #). 

Within  the  sphere  with  radius  p'  drawn  round  about  B  of  Fig.  I  the  final 
position  of  rest  of  the  electron,  we  find  the  ordinary  electrostatic  field. 
Without  the  sphere  with  radius  p,  drawn  about  o,  where  the  collision  at 


THE  STRUCTURE  OF  y  RAYS.  415 

the  moment  /  =  o  began,  we  find  the  electromagnetic  field  accompanying 
the  electron  in  motion.  The  electric  force  E,  pointing  toward  o'  where 
the  electron  at  the  moment  /  would  be,  if  it  had  not  been  stopped,  is 
equal  to 

'  e(i  -  p)  .""I 

r2(i  - /32  sin2  <?)*'  c' 

The  component  En  of  E  in  the  direction  p  is  equal  to 

_  e(i  -  p)r  cos  (y  -  0) 
r*(i  -  p  sin2  rf*       ' 

r  cos  (<p  —  &)  =  p(i  —  |8  cos  #), 
r*(i  -  p  sin2  p)*  =  P3(i  -  0  cos  tf)3, 


P2(i  -  0  cos  tf)2 ' 

We  shall  now  calculate  the  tangential  electric  force  Et  in  the  shell.  In 
Fig.  I  we  consider  the  volume  cut  out  of  the  shell  by  a  cone  with  an  angle 
$.  As  there  are  no  charges  within  this  cap,  the  resultant  flux  of  the 
electric  force  flowing  out  of  the  volume  must  be  equal  to  zero.  The 
inflowing  flux  0i  is  due  to  the  component  Et'  and  to  the  force  efp'2  or 
approximately  e/p2 

e 
0i  =  Etd2Trp  sin  $  H — -27rp(p  —  p  cos  #), 

=  Etd2irp  sin  &  -f-  e2ir(l  —  cos  $). 
The  outflowing  flux  02  is  due  to  the  force  En  and  is  equal  to 

C^  -r 

02  =          En2irp  sin  &d&  •  p 
Jo 

sin 


-  p  cos  #r 

I    —  COS  & 
1—0  COS  I? 

01    =    02» 

hence 

I  —  cos 


Etd2irp  sin  #  +  e27r(l  —  cos  #)  =  e(l  +  /3)27r 


I  —  j8  cos 
sin  #  ez;  sin  z? 


5p(i  —  0  cos  $)        dp(c  —  v  cos  #)  ' 

In  every  electromagnetic  disturbance  the  electrostatic  energy  is  equal 
to  the  magnetic  energy.     This  is  the  case  if  we  assume  for  the  magnetic 


4  '  6  JAKOB  KUNZ.  [iS?Es°. 

force  H  in  the  pulse  the  expression 

H  =  cEt. 

The  distribution  of  the  lines  of  force  is  shown  in  Fig.  2,  and  in  Fig.  3 
for  the  limiting  case  where  the  velocity  v  becomes  equal  to  the  velocity 


Fig.  2.  Fig.  3. 

c  of  light.  We  see  from  these  figures  that  with  increasing  velocity  v 
the  electric  force  Et  becomes  a  maximum  in  a  certain  direction  #m  where 
most  of  the  energy  flows  away  from  the  electron,  and  that  in  the  limit 
for  v  =  c  the  energy  flows  out  in  the  direction  $m  =  o,  that  is  in  the 
direction  of  motion  of  the  electron.  When  the  velocity  v  is  so  small  that 
it  can  be  neglected  with  respect  to  c,  then  on  the  contrary,  the  maximum 
of  the  energy  radiates  away  from  the  electron  in  the  equatorial  plane. 

ev2  sin  $ 

lp(c  —  v  cos  d)(2c  —  v  cos  #)  ' 
If  we  neglect  at  first  the  change  in  the  factor  i/(2c  —  v  cos  #),  we  get 

ev2  sin  & 
lp(c  —  v  cos  #) 
and 

8Et  _    e  v2(c  vos  &  —  v) 

~d&  ==  ~fy  (c  -  v  cos  &Y ' 

which  vanishes  when  cos  #  =  v/c;  for  this  angle  the  electric  force  is  a 
maximum  and  the  energy  radiating  away  from  the  electron  becomes 
approximately  a  maximum  also. 

When     -  =  0.9       then     tf  =  25°  45', 

v 

when      -  =  0.99     then     &  =  8°  and  when 

c 

-  =  i          then     tf  =  o°. 
c 


No^dY1']  THE  STRUCTURE  OF  y  RAYS.  417 

The  effect  becomes  marked  only  when  the  velocity  v  approaches  that  of 
light.  Returning  to  the  complete  expression  Et,  we  find  that  it  becomes 
a  maximum  for  the  angle  &  determined  by 

/          c2\  c 

cos3  $  -  2  1  i  +  —  I  cos  tf  +  3-  =  o. 

For 

C          IO 

v=~-~^> 

the  three  roots  are  —  2.42,  1.497  and  0.9210,  hence  the  angle  #  =  22°  55', 
But  as  the  shell  has  not  everywhere  the  same  thickness,  this  angle  does 
not  accurately  indicate  the  direction  in  which  most  of  the  energy  is 
radiated  away. 

The  energy  of  the  electric  force  Et  within  the  elementary  volume  2irp 
sin  dpddd  is  equal  to 

dEes  =  --E?2irp  sin  dpd$8 

oTT 

I  v3  sin3 


4     l(2c  —  v  cos  &)(c  —  v  cos  #)2 ' 

The  electrostatic  energy  in  the  cap  under  the  angle  $  is  given  by  the 
integral 


4 

/     ,/0      (2C  - 

z;  cos  $)(c  — 

V  COS  t?)2 

_I'2| 

3c2  —  i>2  1      c  —  v  cos  # 

4c2  —  z;2  ,      2c 

—  v  cos  i? 

~4ii 

C2            10S 

c  —  v 

c2       log 

2c  —  z; 

+  - 

-z;2r           I 

I 

-.].}• 

c        Lc  —  v 

cos  #       c  — 

The 

function 

sin3 

I? 

(2C 

—  v  cos  #)(c 

:   —  V  COS  #)2 

or 

sin3 

t? 

^     "(»• 

^008  *)( 

V                \2 
I    COS  ^  1 

c           1 

has  been  plotted  in  Fig.  4  for  the  values  v/c  =  9/10  and  v/c  =  99/100. 
This  figure  shows  clearly  that  with  increasing  velocity  the  energy  is 
radiated  away  in  a  direction  which  approaches  more  and  more  the 
direction  of  motion  of  the  electron.  The  bearing  of  this  conclusion  on 
the  fluctuations  of  Schweidler  and  perhaps  on  the  difference  in  the 


JAKOB  KUNZ. 


SECOND 
SERIES. 


photoelectric  effect  according  to  the  incidence  of  the  beam  of  light,  or 
Roentgen  rays  is  obvious.  If  we  attribute  to  the  electromagnetic  field 
not  only  energy,  but  also  momentum  and  mass,  then  it  follows,  that  the 
electromagnetic  mass  of  the  electron,  when  it  comes  to  rest,  is  thrown 


Fig.  4. 

forward  more  and  more  with  increasing  velocity.  This  electromagnetic 
mass  and  momentum  concentrated  in  a  comparatively  small  space,  is 
not  so  very  different  from  the  notion  of  light  particles  in  the  old  emission 
theory. 

UNIVERSITY  OF  ILLINOIS, 

LABORATORY  OF  PHYSICS, 
May  22,  1915. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.  S.,  Vol.  VII,  No.  i,  January,  1916.] 


ON  THE  CONSTRUCTION  OF  SENSITIVE   PHOTOELECTRIC 

CELLS. 

BY  JAKOB  KUNZ  AND  JOEL  STEBBINS. 

THE  high  sensitiveness  of  photoelectric  cells  of  alkalihydrides  has 
been  discovered  by  Elster  and  Geitel.  For  several  years  we  have 
tried  to  apply  this  cell  in  stellar  photometry.  J.  G.  Kemp1  and  W.  F. 
Schulz2  have  shown  that  it  is  possible  and  advantageous  to  replace  the 
selenium  in  stellar  photometry  by  the  photoelectric  cell.  Practically  at 
the  same  time  corresponding  measurements  have  been  made  in  Germany, 
especially  in  the  observatory  of  Berlin. 

One  of  us  has  reported  on  an  astronomical  discovery  made  by  the 
photoelectric  cell  in  the  Evanston  meeting  of  the  American  Astronomical 
Society  in  September,  1914.  In  the  last  two  years  we  have  tried  to 
improve  the  photometric  properties  of  the  cell  and  we  have  arrived  at  a 
form  which  seems  to  be  satisfactory  with  respect  to  sensitiveness,  con- 
stancy, absence  of  the  dark  current,  etc.  The  final  form  is  indicated  by 
Fig.  i,  which  is  drawn  full  size.  The  glass  bulb  is  3.4  cm.  in  diameter. 


It  contains  a  small  platinum  cathode  C,  a  platinum  ring  of  1.8  cm.  in 
diameter  as  an  anode  A,  which  passes  through  a  platinum  cylinder  B] 
this  cylinder  was  found  to  be  very  necessary  in  order  to  lead  surface  and 
electrolytic  currents  of  the  glass  to  earth.  Strips  of  tinfoil  were  occa- 
sionally wrapped  around  the  glass  cylinder  at  D  and  the  cathode  C,  in 
order  that  dark  currents  might  be  suppressed.  The  tubes  are  connected 
to  the  mercury  pump  and  heated  two  to  three  hours  to  330°  C.  to  drive 
off  the  remaining  gases.  A  small  quantity  of  the  pure  alkali  metal  is 
distilled  on  the  silver  mirror  of  the  cell,  which  is  kept  cool  by  cold  water 
or  ice,  at  the  same  time  the  end  AD  of  the  cell  is  heated  from  160  to  240°, 
according  to  the  alkali  metal,  by  means  of  a  heating  coil. 

1  J.  G.  Kemp,  PHYS.  REV.,  Vol.  I.,  p.  274,  1913. 

«  W.  F.  Schulz,  Astrophysical  Journal,  Vol.  XXXVIII,  p.  187. 


63  JAKOB   KUNZ   AND   JOEL   STEBBINS.  [IS?Es! 

The  most  sensitive  cells  have  been  obtained  when  the  metal  was 
deposited  in  a  thin  uniform  layer.  Pure  hydrogen  from  palladium  was 
then  admitted  and  its  pressure  so  adjusted  that  a  potential  difference 
of  280  to  400  volts  between  the  electrodes  produced  a  uniform  glow 
discharge.  Often  a  spark  or  arc  appears  instead  of  the  bright  uniform 
glow,  and  the  spark  is  apt  to  destroy  the  sensitive  layer.  By  experience 
one  finds  the  best  conditions  for  the  glow  to  appear.  The  sensitiveness 
will  be  tested  during  the  formation  of  the  hydride.  As  a  rule  the  forma- 
tion requires  only  one  to  three  seconds  for  the  maximum  sensitiveness; 
if  continued,  the  colors  of  the  compound  change  and  the  deflection  in 
the  galvanometer  decreases.  During  the  formation  the  electrode  C  is 
negative  and  A  positive.  But  in  certain  gases  like  ammonia  and  ethane 
a  sensitive  layer  is  also  formed  if  the  current  is  reversed.  After  the 
formation  the  gas  is  carefully  pumped  out  and  replaced  by  an  inert  gas, 
helium,  argon,  or  neon.  The  pressure  is  so  chosen  as  to  get  a  maximum 
sensitiveness. 

Experiments  have  been  made  with  the  object  of  finding  out  the 
influence  of  the  size  and  shape  of  the  cell  on  the  sensitiveness.  The 
diameter  varied  from  5  to  2.5  cm.  and  the  sensitiveness  rather  increased 
with  decreasing  diameter.  The  silver  mirror  was  sometimes  deposited 
on  a  flat  or  conical  bottom,  so  that  the  incident  light  should  be  reflected 
and  its  action  increased;  but  very  little  increase  in  the  deflection  of  the 
galvanometer  was  observed,  so  that  the  ordinary  spherical  shape  was 
chosen. 

Efforts  have  been  made  to  replace  the  hydrogen  by  other  gases,  for 
instance  ethane,  ammonia  and  acetylene.  With  ethane  and  the  current 
reversed  a  very  dark  violet-blue  color  was  obtained  of  a  high  sensitive- 
ness, and  of  a  beautiful  metallic  luster,  but  unfortunately  the  sensitive- 
ness proved  not  to  be  constant.  When  dry  ammonia  vapor  was  used 
instead  of  hydrogen  for  the  formation,  a  bright  blue  layer  was  obtained 
of  high  sensitiveness  which  however  decayed  also  in  the  course  of  time. 
Acetylene  finally  formed  a  black  layer  with  potassium  under  the  influence 
of  the  electric  field,  but  it  was  very  little  sensitive.  So  far  hydrogen 
seems  to  give  the  most  sensitive  and  the  most  constant  cells. 

Four  alkali  metals  have  been  used,  viz.,  sodium,  potassium,  rubidium 
and  caesium.  The  best  results  have  been  obtained  with  rubidium  and 
neon.  The  metal  was  distilled  in  the  cell  while  the  silver  mirror  was 
cooled  with  ice.  A  potential  difference  of  280  volts  produced  a  glow  in 
the  hydrogen  and  a  very  beautiful  violet  reddish  sensitive  layer  with  a 
bright  metallic  luster.  The  hydrogen  was  then  replaced  by  helium, 
argon  or  neon.  The  neon  was  received  from  the  Bureau  of  Standards. 


VOL.  VII.1 
No.  i. 


SENSITIVE   PHOTOELECTRIC   CELLS. 


64 


The  three  curves  A,  B  and  C,  of  Fig.  2  show  the  relative  sensitiveness 
of  the  rubidium  cells  filled  with  these  three  gases.  Helium  gives  the 
smallest,  neon  the  best  sensitiveness.  Nevertheless  it  is  possible  that 
the  helium  and  argon  cells  are  better  than  the  neon  cell  because  the 
curve  for  the  neon  rises  much  quicker  than  the  other  curves,  in  other 
words  the  neon  cell  is  more  sensitive  to  small  changes  of  the  potential 
difference  acting  between  the  electrodes  than  the  helium  and  argon  cell. 
It  is  very  important  to  use  perfectly  pure  gases. 

The  sensitiveness  of  some  cells  decays  slightly  during  the  first  few 
days  after  the  formation  and  then  becomes  constant.  Some  distinct 
white  spots  appeared  on  the  surface  of  some  of  the  very  bright  violet 
rubidium  metals,  and  in  one  or  two  instances  such  a  spot  became  wider 


Fig.  2. 

in  the  course  of  time  and  covered  finally  the  whole  surface,  which  then 
appeared  bright  bluish,  and  whose  sensitiveness  was  considerably  less 
than  that  of  the  original  violet  surface.  When  the  cells  were  of  a  larger 
size,  these  bright  violet-red  surfaces  on  rubidium  were  never  obtained, 
but  rather  sky-blue  and  blue-green  colors  which  exhibit  very  beautiful 
iridescence.  The  potassium  cells  were  formed  with  a  potential  difference 
of  360  volts.  The  glow  discharge  gives  almost  instantly  rise  to  a  most 
beautiful  golden  rose  color,  which  is  exceedingly  sensitive,  but  not  very 
stable.  When  the  formation  is  continued  for  a  second  or  two,  a  deeper 
violet-red  appears  which  remains  practically  constant,  but  the  golden 
hue  gradually  fades  away.  The  sensitiveness  of  the  cell  when  filled 
with  the  different  gases  is  shown  by  the  curves  of  Fig.  3.  Neon  again 


JAKOB   KUNZ   AND   JOEL   STEBBINS. 


[SECOND 

[SERIES. 


shows  the  greatest  sensitiveness,  hydrogen  the  smallest,  argon  seems  to 
give  a  curve  which  lies  between  A  and  B,  but  this  question  is  not  quite 
settled.  A  comparison  of  Figs.  2  and  3  shows  that  for  rubidium  we  find 
the  same  photoelectric  current  with  a  potential  difference  about  40 
volts  smaller  than  for  potassium.  Very  striking  iridescence  can  be 
obtained  by  the  potassium. 

Cells  have  also  been  formed  with  sodium  and  caesium.  The  former 
metal  gives  very  sensitive  cells,  but  their  construction  is  more  difficult 
than  that  of  the  potassium  and  rubidium  cells,  the  sodium  seems  to  act 
somewhat  on  the  silver  mirror,  so  that  the  distilled  metal  does  not  seem 
so  bright  on  the  silver  as  on  the  glass.  If  however,  the  metal  is  distilled 
on  the  glass  bulb  directly,  then  the  contact  with  the  electrode  is  un- 
satisfactory. The  pure  metal  seems  to  give  a  very  sensitive  golden 


toe 


Fig.  3. 

layer.  The  caesium  finally  is  liquid  at  28°  and  can  therefore  not  be  used 
directly.  A  solid  amalgam  of  this  alkali  metal  has  been  formed  which 
was,  however,  of  a  rather  weak  sensitiveness. 

The  cells  described  in  this  article  show  a  very  small  dark  current;  if 
it  exists  at  all,  it  can  be  compensated  by  the  application  of  a  convenient 
small  potential  at  the  platinum  cylinder  between  the  two  electrodes. 
As  far  as  our  present  measurements  indicate,  there  is  an  accurate  pro- 
portionality between  the  intensity  of  the  incident  light  and  the  photo- 
electric current.  The  cells  are  used  in  stellar  photometry. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
August  12,  1915. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S..  Voi.  VII,  Nc.  i,  January,  1916.] 


AN  INVESTIGATION  OF  THE  TRANSMISSION,  REFLECTION 

AND   ABSORPTION    OF   SOUND    BY   DIFFERENT 

MATERIALS. 

BY  F.  R.  WATSON. 

THE  experiments  on  the  transmission  of  sound  were  performed  with 
the  following  arrangement  of  apparatus.1  The  source  of  sound 
was  an  adjustable  whistle  blown  by  air  from  a  constant  pressure  tank 
and  mounted  at  the  focus  of  a  specially  constructed  parabolic  reflector 
with  a  focal  length  of  nine  inches  and  an  aperture  of  five  feet.  This  was 
placed  in  front  of  an  open  doorway  so  that  the  sound,  which  proceeded 
in  a  large  parallel  bundle  from  the  reflector,  could  pass  through  the 
doorway  into  another  room.  The  receiver  of  sound,  a  Rayleigh  resonator, 
was  mounted  in  the  other  room  in  the  path  of  the  sound  symmetrically 
opposite  the  reflector  and  doorway  and  measured  the  intensity  of  the 
transmitted  sound. 

The  resonator  used  was  a  modification  of  Rayleigh 's  original  design.2 
It  consisted  of  a  horizontal  brass  tube  closed  at  one  end  by  an  adjustable 
piston.  A  mica  disc  was  suspended  by  a  quartz  fiber  at  an  angle  of  45° 
with  the  axis  of  the  tube.  When  the  sound  of  the  whistle  reached  the 
resonator  it  set  up  a  back-and-forth  surging  of  the  air  in  the  resonator 
and  caused  the  mica  disc,  which  was  placed  at  a  loop,  to  rotate.  This 
action  is  in  accordance  with  the  general  principle  that  any  flat  object 
in  a  current  of  air  tends  to  set  itself  at  right  angles  to  the  current.  The 
amount  of  rotation  was  measured  by  means  of  a  lamp  and  scale  in  con- 
nection with  a  mirror  which  was  attached  to  the  suspended  system  above 
the  mica  disc. 

The  readings  on  the  scale  are  proportional,  for  small  angles  of  rotation 
of  the  disc,  to  the  intensity  of  the  sound.  This  is  shown  as  follows. 
The  moment  M  of  the  couple  turning  the  disc  may  be  proven3  to  be 

M  =  kW2  sin  2(0  -  <p), 

where  W  is  the  velocity  of  the  steam,  6  is  the  angle  of  repose  between 
the  direction  of  the  stream  and  the  normal  to  the  disc,  <p  is  the  angle  of 

1  PHYS.  REV.,  Vol.  V.,  p.  342,  1915. 

2  Phil.  Mag.,  Vol.  14,  p.  186,  1882. 

3  W.  Konig,  Wied.  Ann.,  Vol.  43,  p.  51,  1891. 


126  F.   R.    WATSON. 

deflection,  and  k  is  a  constant.  In  case  the  stream  is  not  steady  but 
alternating,  as  it  would  be  in  the  case  of  the  vibrating  air  in  the  resonator, 
W*  may  be  replaced1  by  the  mean  value  of  W2.  The  intensity,  /,  of 
the  sound  setting  up  the  vibrations  in  the  resonator  is  proportional  to 
the  square  of  the  velocity,2  so  that 

M  =  ki  I  sin  2(6  —  <p). 

Finally  the  turning  couple  M  becomes  equal  for  equilibrium  to  the 
restoring  couple  set  up  by  the  twisted  quartz  fiber  and  this  latter  couple 
is  proportional  for  small  angles  of  rotation  to  the  angle  of  rotation  <p,  or 

M  =  k*<p. 
Comparing  the  intensities  of  two  sounds  we  get 

Ii  =  <pi    sin  2(0  -  g>2) 
/2  ~  <p2     sin  2(0  -  <pi)  ' 

In  the  experimental  observations,  <p  was  not  measured  directly; 
since  the  scale  readings  are  proportional  to  tan  2p,  the  scale  being  plane 
and  the  angle  of  deflection  being  doubled  by  the  reflection  of  the  spot  of 
light  from  the  mirror.  Calculations  for  the  data  taken  show  that  the 
ratios 

tan  2  (pi 

tan  2(pz 
and 

<pi  sin  2(0  -  (00 


<P2  sin  2(0  -  <pi) 

differ  about  2  per  cent,  for  the  maximum  angle  of  deflection,  1  1°.  There- 
fore, as  stated,  the  readings  on  the  scale  may  be  taken  as  proportional 
to  the  intensity  of  the  sound. 

Measurements  were  taken,  first,  through  the  open  doorway,  then  with 
one  panel  of  material  placed  over  the  doorway,  then  two  panels  and 
finally  three  panels;  the  deflection  of  the  resonator  being  noted  for  each 
case.  Considerable  trouble  was  experienced  in  getting  steady  deflections 
of  the  resonator.  This  was  finally  overcome  to  a  great  extent  by  arrang- 
ing a  delicate  adjustment  for  keeping  constant  the  flow  of  air  to  the 
whistle,  and  also  by  building  a  small  house  with  a  glass  window  for  the 
observer.  Any  movement  of  articles  or  air  in  the  room  changed  the 
deflection  of  the  resonator  so  that  rigid  observance  of  immovability 
of  objects  was  necessary.  The  samples  to  be  tested  were  mounted  on 
similar  frames  of  one-inch  cypress  strips  and  fastened  over  the  open 

1  Rayleigh,  Th.  of  Sound,  Vol.  II.,  p.  44. 

2  Rayleigh,  Th.  of  Sound,  Vol.  II.,  p.  16,  and  Zernov,  Ann.  der  Phys.,  Vol.  26,  p.  79,  1908. 


VOL.  VII 
No.  i. 


]      TRANSMISSION   OF   SOUND   BY  DIFFERENT   MATERIALS.        12/ 


doorway  by  two  ropes.  A  strip  of  hairfelt  was  mounted  around  the 
woodwork  of  the  doorway  to  prevent  sound  leaking  through  at  the 
edges.  Preliminary  measurements  were  carried  on  for  some  time  to  get 
the  apparatus  and  method  of  taking  observations  in  satisfactory  shape. 
On  December  30,  two  complete  sets  of  observations  were  taken,  the 
average  of  these  being  used  to  obtain  the  comparative  values  of  the 
transmission  powers  of  the  different  materials.  Table  I.  gives  the 
results  obtained. 

TABLE  I. 

Transmission  of  Sound. 


Material. 

Deflection  of  Resonator  in 
Centimeters. 

Average  Deflection. 

Thickness  in  Layers. 

0 

i 

2 

3 

o 

i 

2 

3 

Open  doorway                           I 

40.3 
38.5 

23.0 
22.3 
7.7 
8.1 
1.1 
1.2 
5.7 
4.3 
7.1 
5.9 
2.2 
2.3 
0.4 
0.25 
0.2 

15.3 
15.5 
3.6 
3.9 
2.1 
2.0 
22.3 
21.1 
2.0 
1.9 
0.5 
0.6 

10.8 
9.9 
2.9 
2.9 
1.0 
0.7 
4.4 
3.2 
0.5 
0.3 
0.1 
0.1 

39.4 

22.6 
7.9 
1.15 
5.0 
6.5 
2.25 

0.32 
0.2 

15.4 
3.75 
2.05 
21.7 
1.95 
0.55 

10.4 
2.9 
0.85 
3.8 
0.4 
0.1 

Y2"  hairfelt  X 

J4"  cork  board                          X 

%"  cork  board             .            X 

%"  paper-lined  hairfelt  X 
%"  paper-lined  hairfelt  X 
%"  flax  board  X 

M"  pressed  fiber  X 

%"  pressed  fiber  

Table  II.  gives  the  calculated  percentages  of  the  sound  transmitted 
and  the  sound  stopped,  it  being  assumed  that  the  open  doorway  trans- 
mits 100  per  cent,  or,  that  it  stops  o  per  cent. 

The  data  of  Table  II.  are  shown  in  the  form  of  curves  in  Fig.  i.  In- 
spection of  these  curves  shows  that  J/£  in.  hairfelt  stops  less  sound  than 
the  other  materials,  one  layer  stopping  only  43  per  cent.  Next  comes 
the  J4  in.  cork  board  which  stops  80  per  cent,  for  one  layer  and  90.5  per 
cent,  and  92.6  per  cent,  for  two  and  three  layers  respectively.  This  is 
followed  by  the  %  in.  paper  covered  hairfelt,  the  %  in.  flax  board  and 
finally  the  %  in.  pressed  fiber,  one  layer  of  which  stops  practically  all 
the  sound.  These  values  do  not  tell  the  whole  story  concerning  the 
acoustical  efficiency  of  the  materials,  since  other  qualities  must  also  be 
considered.  The  pressed  fiber,  for  instance,  is  of  little  value  acoustically 
because  its  sound  absorbing  power  is  very  small. 


F.    R.    WATSON. 


[SECOND 

[SERIES. 


TABLE  II. 

Transmission  of  Sound  Through  Different  Materials. 


Material. 

Percentage  of  Sound. 

Transmitted. 

Stopped. 

Thickness  in  Layers  

0 

I 

2 

3 

0 

I 

2 

3 

Open  doorway 

100 

57.0 
20.0 
2.9 
13.0 
1.7 
5.7 
0.08 
0.05 

39.0 
9.5 

5.2 
55.0 
0.5 
0.14 

26.0 
7.4 
2.2 
9.6 
0.1 
0.02 

0 

43.0 
80.0 
97.1 
87.0 
98.3 
94.3 
99.9 
99.9 

61.0 
90.5 
94.8 
45.0 
99.5 
99.8 

74.0 
92.6 
97.8 
90.4 
99.9 
99.9 

Yz"  hairfelt  

i^"  cork  board 

Y±'  cork  board  

3^"  paper  lined  hairfelt  

Y±'  paper  lined  hairfelt  
%"  flax  board  

%."  pressed  fiber 

%"  pressed  fiber  

Thickness  of  Material  in  Layers 


Fig.  1. 

Percentage  of  sound  stopped  by  materials. 
Curves  showing  the  percentage  of  sound  stopped  by  different  materials. 

The  curves  for  the  J4  m-  paper-lined  hairfelt  show  that  this  sample 
acts  differently  than  the  others.  Two  layers  of  this  material  stop  less 
sound  than  one  layer.  Repeated  measurements  gave  the  same  puzzling 
result.  The  %  in.  cork  board,  shows  the  same  phenomenon,  but  to  a 
less  degree.  After  some  consideration,  it  was  decided  to  investigate 
other  acoustical  properties  of  the  samples  to  see  if  additional  data  would 
explain  this  anomalous  transmission. 

If  incident  sound  falls  on  a  material,  three  things  may  happen.  The 
sound  may  be  partly  reflected,  partly  absorbed  and  the  rest  transmitted. 
If  these  three  fractions  are  added  together,  they  must  equal  the  incident 
sound,  or 


No"iVH']      TRANSMISSION   OF   SOUND    BY   DIFFERENT   MATERIALS.        I  2Q 

T  +  A  +  -R  =  I  =  100  per  cent. 

Therefore  to  know  what  happens  to  the  incident  sound  it  is  necessary  to 
determine  the  amounts  reflected,  absorbed  and  transmitted.  On  con- 
sidering the  case  of  the  paper-lined  hairfelt  in  the  light  of  this  reasoning, 
it  was  decided  to  attempt,  to  measure  the  reflection  of  sound. 


REFLECTION  OF  SOUND. 

By  moving  the  parabolic  reflector  off  to  one  side,  the  sound  was  sent 
obliquely  toward  the  open  doorway  where  it  was  reflected  by  the  hairfelt 
and  then  passed  to  the  Rayleigh  resonator  which  had  been  moved  into 
the  same  room  with  the  reflector  and  placed  so  as  to  be  directly  in  the 
path  of  the  reflected  sound.  The  observer,  as  in  the  transmission  tests, 
stationed  himself  inside  the  small  house  and  read  the  deflection  of  the 


Fig.  2. 
Action  of  a  material  in  reflecting,  absorbing  and  transmitting  sound. 

resonator  through  the  glass  window.  A  small  portion  of  sound  was 
reflected  from  the  sides  of  the  doorway  so  that,  even  with  no  material 
over  the  open  door  space,  the  resonator  gave  a  small  deflection.  This 
was  taken  as  the  zero  deflection  for  the  other  readings.  The  deflection 
for  100  per  cent,  reflection  was  arbitrarily  taken  to  be  the  largest  deflec- 
tion obtained,  namely,  the  deflection  given  by  one  layer  of  %  in.  cork 
board.  This  value  is  doubtless  too  small,  but  probably  not  much 
in  error,  especially  when  only  comparative  values  are  being  considered. 
The  average  of  two  sets  of  observations  on  the  reflection  of  sound  from 
the  materials  is  given  in  Table  III.  and  in  curves  in  Fig.  3.  The  inter- 
pretation of  the  results  is  best  realized  by  combining  curves  from  Figs, 
i  and  3.  Thus,  for  %  in.  hairfelt  in  Fig.  4,  it  is  seen  that  the  curve  for 
the  reflected  sound  follows  very  closely  the  curve  for  the  stopped  sound. 
Consideration  of  Fig.  2  shows  that  the  sound  which  is  stopped  by  the 
material  is  reflected  and  absorbed. 
The  amounts  of  reflected,  absorbed  and  transmitted  sound  are  thus 


130 


F.    R.    WATSON, 


[SECOND 

[SERIES. 


TABLE  III. 

Reflection  of  Sound  by  Different  Materials. 


Material. 

Deflection  of  Resonator  in 
Centimeters. 

Percentage  of  Sound 
Reflected. 

Thickness  in  Layers. 

o 

i 

2 

3 

o 

I 

2 

3 

Open  doorway  

3.9 

4.9 
15.7 
25.9 
20.7 
10.4 
22.5 
23.2 

6.6 
22.0 
21.2 
5.9 
6.6 
20.0 

10.5 
22.6 
22.1 
10.0 
9.3 
20.0 

0 

19 
61 
100 
80 
40 
87 
90 

25 
85 
82 
23 

25 

77 

40 
87 
85 
39 
36 
77 

H"  hairfelt 

%"  cork  board  

%"  cork  board.            

\£."  paper  lined  hairfelt 

%"  paper  lined  hairfelt  
%"  flax  board 

W  pressed  fiber  

Thickness  of  Material  in  Layers 
Fig  3.-  Percentage  of  Sound  Reflected  by  Materials 

Fig.  3. 
Curves  showing  the  percentage  of  sound  reflected  by  different  materials. 

easily  shown  in  Fig.  4.  The  amounts  of  sound  reflected  and  absorbed 
increase  with  the  thickness,  but  the  transmission  decreases.  It  should 
be  remembered  that  the  absolute  values  for  the  absorption  and  reflection 
are  doubtless  in  error  but  that  the  comparative  values  are  in  correct 
proportion. 

The  curves  for  the  %  in.  paper-lined  hairfelt  are  shown  in  Fig.  5. 
The  two  curves  of  reflection  and  transmission  follow  each  other  closely. 
It  is  interesting  to  note  how  the  absorption  increases  uniformly  although 
the  transmission  and  reflection  both  vary.  The  probable  cause  for  the 
anomalous  reflection  and  transmission,  as  will  be  discussed  later,  lies 
in  the  vibration  of  the  material  due  to  resonance.  Certain  thicknesses 
of  the  material  vibrate  vigorously  under  the  action  of  the  sound  and  thus 


VOL.  VII. 
No.  i. 


]       TRANSMISSION   OF   SOUND   BY   DIFFERENT  MATERIALS. 


create  sound  waves  on  the  further  side  of  the  material.  This  explanation 
is  advanced  also  by  Weisbach1  who  made  a  similar  test  but  with  different 
apparatus  and  method. 


Thickness  in  Layers 


Fig. 4.  -  Curves  for  Hair  Felt,  showing  how  the  Reflection,  Absorption,  and  Tronsmissioo 
vary  with  the  Thickness. 

Fig.  4. 

Curves  for  hairfelt,  showing  how  the  reflection,  absorption  and  transmission  vary  with  the 

thickness. 

DISCUSSION  OF  RESULTS. 

The  transmission  of  sound  of  constant  pitch  depends  on  at  least  three 
qualities  of  the  transmitting  material  ;• — its  porosity,  density  and  elas- 
ticity. Porous  bodies  transmit  sound  in  much  the  same  proportion  that 


Thickness  in  Layers 


Fig.5  -Showing  the  Reflection,  Absorpf  ion.  and  Transmission 
of  Sound  byjj'poperlioed  hair-felt. 

Fig.  5. 
Showing  the  reflection,  absorption  and  transmission  of  sound  by  %!'  paper-lined  hairfelt. 

^'Versuche  iiber  Schalldurschlassigkeit,  Schallreflexion  und  Schallabsorption,"  Annalen 
der  Physik,  Vol.  33,  p.  763,  1910. 


132  F.   R.    WATSON. 

they  transmit  air.1  This  is  why  hairfelt  transmits  more  sound  than  the 
other  samples.  Density  also  plays  a  part.  Two  samples  stop  sound 
in  proportion  to  their  densities,  other  conditions  being  equal.2  Thus 
the  pressed  fiber  stops  more  sound  than  the  same  thickness  of  cork 
because  it  is  heavier.  Finally,  an  elastic  body  may  transmit  sound  if  it 
happens  to  be  in  tune  with  the  source  of  sound  so  as  to  vibrate.  To 
make  this  clear,  consider  the  material  to  form  a  wall  in  the  path  of  the 
sound  and  imagine  it  to  vibrate  exactly  as  the  air  would  if  the  material 
were  not  present.  Under  these  circumstances,  there  would  be  no 
reflection  but  only  transmission  of  sound.  From  the  results  obtained  it 
seems  probable  that  two  layers  of  paper  lined  hairfelt  approximate  to 
such  a  vibration. 

In  case  the  pitch  of  the  sound  varies,  porous  walls  and  elastic  walls 
reflect  high  pitched  sounds  in  greater  degree  than  low  pitched  ones.3 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS. 

1  Tufts,  Amer.  Jour,  of  Science,  Vol.  2,  p.  357,  1901. 

2  Jager,  "Zur  Theorie  des  Nachhalls,"  Sitzber.  der  Kaiserl.  Akad.  der  Wissenschaften  in 
Wien,  Math-naturw.  Klasse;  Bd.  CXX.,  Abt.  Ila,  Mai,  1911. 

8  Jager,  loc.  cit. 


A  STUDY  OF  RIPPLE  WAVE  MOTION. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  VII,  No.  2,  February,  1916.] 


A  STUDY  OF  RIPPLE  WAVE  MOTION. 

BY  F.  R.  WATSON  AND  W.  A.  SHEWHART. 

\  ^  7AVE  motion  has  been  made  the  object  of  a  large  number  of  theo- 

*  *  retical  and  experimental  investigations  to  determine  the  physical 
properties  of  waves  and  also  to  explain  the  various  phenomena  of  re- 
flection, refraction,  diffraction  and  interference.  One  of  the  most 
satisfactory  experimental  methods  of  attack  has  been  found  in  the  study 
of  ripple  waves,  since  in  this  case,  we  can  visualize  almost  every  phenom- 
ena of  wave  motion. 

The  object  of  this  paper  is  to  describe  the  development  of  a  method  by 
which  ripple  waves  may  be  generated  not  only  in  steady  patterns  but 
also  in  patterns  in  which  the  waves  apparently  move  very  slowly.  This 
allows  a  leisurely  examination  of  the  various  phenomena.  The  method 
also  allows  the  convenient  exhibition  of  the  waves  to  a  lecture  audience. 

Historically,  the  investigation  of  ripples  began  in  1871  when  Lord 
Kelvin1  observed  that  the  propagation  of  ripples  depended  on  surface 
tension.  Matthieson2  tested  the  validity  of  Kelvin's  formula,  but,  because 
of  the  rough  measurements  of  the  waves  set  up  by  a  pin  point  piercing 
a  jet  of  water,  failed  to  obtain  a  great  degree  of  accuracy.  Ahrendt,3 
Riess4  and  others  made  similar  experiments,  but  it  remained  for  Lord 
Rayleigh5  to  develop  the  first  accurate  method  of  investigation.  To 
make  visible  the  extremely  small  disturbances  in  the  plane  of  the  liquid 
surface,  he  used  a  modified  form  of  Foucault's  method  of  testing  plane 
surfaces.  Furthermore,  he  used  the  stroboscopic  method  for  making 
the  waves  appear  to  stand  still.  Dorsey6  and  Watson7  have  extended  and 
improved  Rayleigh's  method  in  making  investigations  on  the  surface 
tension  of  liquids. 

Tyndall8  first  made  use  of  ripple  waves  to  illustrate  wave  motion. 
Later,  Vincent9  was  able  with  more  refined  apparatus  to  obtain  beautiful 
photographs  of  the  same  phenomena.  H.  Schultze10  devised  an  electrical 

1  Phil.  Mag.  (4),  Vol.  42,  p.  375.  1871. 

2  Wied.  Ann.,  Vol.  38,  p.  118,  1889. 

3  Exner's  Rep.  der  Physik,  Vol.  24,  p.  318,  1888. 
4Exner's  Rep.  der  Physik,  Vol.  26,  p.  102,  1890. 

6  Lord  Rayleigh's  Collected  Works,  Vol.  III.,  p.  383. 

6  PHYS.  REV.,  Vol.  5,  p.  173,  1897. 

7  PHYS.  REV.,  Vol.  12,  p.  257,  1901. 

8S.  P.  Thompson,  "Light,  Visible  and  Invisible,"  Chap.  i. 
9  Phil.  Mag.,  Vol.  43,  p.  417;  45,  191;  46,  290. 
10Zeitsch.  f.  Instk.,  p.  151,  1907. 


VOL.  VII. 
No.  2. 


A  STUDY  OF  RIPPLE  WAVE  MOTION. 


227 


method  for  producing  ripples,  modifications  of  which  have  been  made 
by  Pfund1  and  Palmer.2  Waetzmann3  developed  a  method  in  which  the 
waves  were  generated  by  intermittent  puffs  of  air,  and  were  made  visible 
by  flashes  of  light  isoperiodic  with  the  puffs.  Waetzmann's  method,  with 
extensions  and  modifications,  has  been  used  in  the  present  investigation. 

Fig.  I  is  a  diagram  of  the 
apparatus.  Ripple  waves  were 
generated  by  puffs  of  air  blown 
against  the  water  surface  in  the 
glass-bottomed  tank  A.  The 
puffs  were  secured  by  cutting  a 
tube  conveying  compressed  air 
and  inserting  in  the  gap  a  disc 
with  a  circular  row  of  equally 
spaced  holes.  When  the  disc 
rotated,  the  current  of  air  was 
periodically  interrupted.  The 
waves  were  made  visible  by  the 
stroboscopic  method.  Light  from 
an  arc  lamp  was  focused  on  the 
row  of  holes  in  the  rotating  disc, 
thus  giving  flashes  isoperiodic 
with  the  puffs  of  air.  By  re- 
flecting the  light  upward  through 
the  glass  tank,  a  steady  pattern 
of  waves  was  revealed.  Fig.  2 
shows  a  photograph  obtained 
with  circular  waves. 

By  using  a  second  row  of  holes, 
which  were  fewer  in  number  than 
those  in  the  row  already  described,  the  flashes  of  light  could  be  made  to 
come  a  little  slower  than  the  puffs  of  air;  the  result  being  that  the  waves 
apparently  moved  forward  slowly.  This  action  allowed  a  leisurely  study 
for  the  different  phases  of  reflection,  diffraction,  etc.,  with  slowly  moving 
waves. 

Trouble  was  experienced  in  getting  steady  patterns  of  waves,  due  to 
vibrations  of  the  apparatus  and  fluctuations  of  the  puffs  of  air.  The 
vibrations  were  overcome  by  mounting  the  tank  on  a  steady  support. 
The  fluctuations  in  the  air  puffs  were  almost  entirely  eliminated  by  using 

1  PHYS.  REV.,  Vol.  32,  p.  324,  1911. 

2  PHYS.  REV.,  Vol.  33,  p.  528,  1911. 

3  Physikalische  Zeitschrift,  Vol.  12,  p.  866,  1911. 


Fig.  1. 

Diagram  of  apparatus  showing  how  ripples  are 
generated  on  a  water  surface  by  puff  of  air  and 
made  visible  stroboscopically  on  the  frosted  glass 
plate  above  the  water  tank. 


228  F.  R.  WATSON  AND  W.  A.  SHEWHART. 

a  cast  iron  disc  10  inches  in  diameter  and  one-fourth  inch  thick  and  facing 
it  after  it  had  been  mounted  on  an  axle  so  that  it  would  run  true.  It  was 
then  mounted  securely  on  a  cast-iron  base  and  rotated  by  a  small  wheel 
on  an  axle  attached  by  a  toggle  joint  to  a  I/6-H.P.  direct-current  motor. 
Variation  of  the  speed  of  the  disc  was  obtained  by  changing  the  resistance 
in  series  with  the  motor  and  also  by  shifting  the  position  of  contact  of 
the  small  wheel  with  the  disc. 

To  make  the  flashes  of  light  sharp  and  definite  in  position,  an  arrange- 
ment of  two  small  screens,  each  pierced  by  a  small  hole,  was  placed  over 
the  edge  of  the  disc  so  that  light  could  pass  only  during  the  instant  that 
a  hole  in  the  disc  came  into  coincidence  with  the  holes  in  the  screens. 
The  reflecting  mirror,  which  was  small  in  area,  was  made  by  polishing 
the  end  of  a  circular  aluminum  rod  cut  at  an  angle  of  45°  to  its  axis. 
The  source  of  light  was  a  carbon  arc  fed  by  a  no-volt  direct  current. 
It  gave  good  illumination  except  for  the  colors  explained  by  Mrs.  Ayrton.1 
These  proved  to  be  troublesome  when  taking  photographs.  A  pattern 
of  waves  that  appeared  well  illuminated  to  the  eye  would  show  serious 
distortions  on  the  photographic  plate. 

The  position  and  form  of  the  aperture  for  the  puffs  of  air  influenced  the 
shape  of  the  waves  to  a  marked  extent.  Satisfactory  results  were  ob- 
tained by  using  a  small  copper  tube  of  about  I  mm.  diameter  placed 
near  the  water  surface.  It  could  easily  be  bent  into  any  desired  position. 

The  waves  may  be  shown  to  an  audience  by  mounting  a  mirror  at  an 
angle  of  45°  over  the  surface  of  the  tank  so  that  the  light  is  reflected  to  a 
screen.  For  this  purpose  it  is  desirable  to  let  more  light  through  so  that 
the  pattern  will  be  well  illuminated.  This  makes  the  definition  of  the 
waves  less  sharp  but  still  satisfactory  enough  for  demonstration. 

Figs.  2  to  7  show  some  of  the  patterns  investigated.  Fig.  4  shows  a 
curious  overlapping  interference.  The  patterns  in  Figs.  5,  6,  and  7  were 
obtained  by  placing  metal  forms  on  the  bottom  of  the  glass  tank  and 
allowing  the  water  surface  to  barely  cover  them.  The  metal  must  be 
free  from  oil  or  grease.  In  Fig.  6  the  diffraction  waves  were  made  more 
intense  by  shielding  the  central  portion  from  the  camera  for  part  of  the 
exposure.  The  time  of  exposure  varied  from  10  seconds  to  20  minutes, 
depending  on  the  amount  of  light.  The  length  of  the  waves  was  measured 
to  be  nearly  0.4  cm. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS. 

x  "The  Electric  Arc,"  Chap.  i. 


Fig.  2. 
Circular  waves. 


Fig.  3. 
Interference  of  two  sets  of  circular  waves. 


Fig.  4. 

Interference  of  two  sets  of  circular  waves 
with  sources  close  together. 


Fig.  5. 

Diffraction  through  a  narrow  channel. 
Also  reflection  of  waves. 


Fig.  6.  Fig.  7. 

Diffraction    of    waves    through    narrow  Reflection   of   waves   in   ellipse, 

and  wide  aperture.  the  conjugate  focus. 

F.  R.  WATSON  AND  W.  A.  SHEWART. 


Note 


[Reprinted from  SCIENCE,  N.  S.,  Vol.  XLIIL,  No. 
1107,  Pages  S93-S94,  March  17,  1916} 


PHOTOGRAPHS   SHOWING  THE  RELATIVE  DE- 
FLECTION   OP    THE    POSITIVE    AND    OF 
THE  NEGATIVE  IONS  AS  COMPARED 
WITH  THAT  OF  THE  ELECTRON 

POSITIVELY  and  negatively  charged  ions, 
atomic  in  size  (commonly  called  "  retrograde 
rays "),  accompany  the  stream  of  electrons 
issuing  from  the  cathode  in  a  highly  exhausted 
discharge  tube.  Thomson1  studied  their  prop- 
erties by  placing  a  photographic  plate  within 
the  tube  in  such  a  position  as  to  receive  these 
rays  after  being  deflected  simultaneously  by 
an  electric  and  a  magnetic  field.  When  the 
fields  are  coincident  (not  crossed)  the  dis- 
placements on  the  photographic  plate  are  in 
directions  at  right  angles  to  each  other.  The 
photographic  method  is  now  in  common  use. 

To  the  writer's  knowledge  no  photographs, 
however,  have  been  published  in  which  all  three 
of  the  component  carriers — the  positive  ion, 
the  negative  ion  and  the  electron — are  shown 
simultaneously  on  the  same  plate.  Since  the 
mass  of  the  electron  is  only  1/1700  that  of  the 
hydrogen  atom,  and  since  the  square  of  the 
magnetic  deflection  varies  inversely  as  the 
mass,  it  follows  that  the  electron  is  driven  off 
the  plate  by  a  magnetic  field  that  would  give 
the  ion  only  an  appreciably  small  deflection. 
By  weakening  the  magnetic  field  the  trace  due 
to  the  electrons  may  be  retained  on  the  plate. 

Two  full-sized  photographs,  Figs.  1  and  2, 
with  key,  Fig.  3,  are  submitted.  Compara- 
tively weak  magnetic  fields  were  employed.2 

1  J.  J.  Thomson,  ' '  Rays  of  Positive  Electricity, ' ' 
pp.  75,  1913. 

2  For  arrangement  of  apparatus  see  C.  T.  Knipp, 
Phys.  Bev.,  Vol.  XXXIV.,  March,  1912. 


The  two  coincident  deflecting  fields  are 
sketched  in  Fig.  3,  in  which  the  direction  of 
the  electrostatic  field  is  indicated  by  the  minus 
and  plus  signs,  while  the  arrow  heads  show 


FIG.  1. 


FIG.  2. 

-jons   -Hons 


-  ^electrons 

FIG.  3. 

the  direction  of  the  magnetic  field.  Again, 
magnetic  deflections  are  up  or  down,  while 
electrostatic  deflections  are  to  the  right  or  left. 
The  undeflected  spot  0  is  due  to  carriers  that 
have  lost  their  charge  before  entering  the  de- 


fleeting  fields.  In  these  photographs,  Figs.  1 
and  2,  the  traces  due  to  the  positive  and  nega- 
tive ions  unite  at  the  central  undeflected  spot, 
the  portion  to  the  right  of  0  being  due  to 
positive  ions  and  that  to  the  left  negative  ions, 
while  the  trace  e,  due  to  electrons,  is  distinctly 
separated  from  0  and  at  some  distance  from 
it,  and  as  we  should  expect,  is  in  the  same 
quadrant  as  the  heavier  negative  ions.  In 
Fig.  1  the  time  of  exposure  was  10  min- 
utes, electrostatic  field  2,070  volts  per  centi- 
meter, magnetic  field  1.7  amperes,  and  the 
vacuum  .011  mm.  mercury;  while  in  Fig.  2 
the  corresponding  values  were  20  min.,  2,070 
volts,  2.25  amperes,  and  .005  mm.  mercury. 
The  effect  of  the  stronger  magnetic  field  is 
distinctly  shown  in  Fig.  2  by  the  increased  dis- 
placement from  0  of  the  trace  due  to  the  elec- 
trons. 

CHAS.  T.  KNIPP 
LABORATORY  OP  PHYSICS, 
UNIVERSITY  OP  ILLINOIS 


[Reprinted  from  SCIENCE,  N.  S.,  Vol.  XLIII.,  No. 
1118,  Pages  787-789,  June  2,  1916] 


ELECTRICAL    DISCHARGE    BETWEEN    CONCEN- 
TRIC CYLINDRICAL  ELECTRODES 

IN  operating  vacuum  tubes  we  invariably 
use  an  induction  coil  or  an  electrostatic  ma- 
chine. The  discharge  in  either  case  is  never 
quite  steady  and  hence  these  methods  of  opera- 
tion do  not  lend  themselves  well  to  a  critical 
study  of  the  growth  of  the  cathode  dark 
spaces.  A  steady,  and  of  course  continuous, 
discharge  may  be  had  if  the  current  is  drawn 
from  a  high  potential  storage  battery.  Ordi- 
narily it  takes  more  cells  than  are  available; 
however,  by  a  right  choice  of  conditions  a 
rather  extended  study  may  be  made  with  di- 
rect current  potentials  of  less  than  1,000  volts. 
The  following  experiments  with  concentric 
cylindrical  electrodes  were  performed  recently 
by  the  writer  in  class  demonstration. 

The  discharge  vessel  consists  of  an  ordinary 
three-quart  battery  jar.  A  hole  bored  through 
the  bottom  receives  the  evacuating  tube,  the 
junction  being  made  airtight  with  ordinary 
sealing  wax.  The  lip  of  the  jar  is  ground  flat 
to  receive  the  plate  glass  lid.  The  junction 
here  is  made  by  means  of  the  frequently  used 
half-and-half  wax,  beeswax  and  resin.  This 
wax  because  of  its  low  melting  point  admits 
of  easy  removal  of  the  glass  plate.  The  elec- 
trodes are  concentric  cylinders  and  may  well 
be  made  of  sheet  aluminum — one  electrode  to 
fit  snugly  the  inner  wall  of  the  jar,  and  the 
other  mounted  on  a  cylinder  of  glass  tubing 
about  li  inches  in  diameter,  which  in  turn  is 
supported  accurately  concentric  by  sealing 
wax  from  the  bottom  of  the  jar.  Outside  con- 
nections to  the  electrodes  are  made  by  fine 
bare  copper  wire  run  out  through  the  waxed 


joints.      The    assembled    discharge    vessel    is 
shown  at  a  in  Fig.  1. 

The  vessel  may  be  exhausted  by  a  Gaede 
mercury  or  a  Gaede  piston  pump  and,  if  de- 
sired, the  vacuum  carried  farther  by  the  use 
of  charcoal  and  liquid  air,  though  the  latter  is 
not  necessary.  The  potential  employed  by 
the  writer  to  produce  the  discharge  was  fur- 
nished by  a  cabinet  of  high  potential  storage 
cells  of  1,000  volts. 


To  pome 


FIG.  1. 


Two  methods  of  operating  were  employed. 
In  the  first  an  adjustable  water  resistance  is 
connected  in  series  with  the  cells  and  dis- 
charge vessel  as  shown  at  Z>  in  Fig.  1.  When 
the  vacuum  is  right  a  beautiful  discharge  will 
make  its  appearance  as  patches  of  light  on  the 
electrodes.  These  patches  of  light,  when  there 
is  considerable  resistance  in  the  circuit  and 
the  vacuum  is  not  very  high,  will  be  opposite 
each  other  and  the  discharge,  as  a  whole,  will 
wander  about,  sometimes  swinging  entirely 
around,  or  at  times  travelling  to  the  edges  of 
the  electrodes,  only  to  break  away  and  move 
to  some  other  point.  The  movement  of  the 
cathode  glow  (which  is  the  smaller  and  hence 
the  brighter)  is  similar  to  that  of  the  cathode 
star  over  the  surface  of  mercury  in  a  mercury 


3 


vapor  lamp.  These  areas  grow  as  the  vacuum 
improves  when  ultimately  the  entire  surface 
of  each  electrode  is  covered.  Or,  with  the 
vacuum  kept  constant,  the  areas  may  be  made 
to  increase  in  size  by  cutting  out  resistance. 
Hence  by  improving  the  vacuum  and  at  the 
same  time  cutting  out  resistance  the  dis- 
charge, if  the  inner  cylinder  is  made  cathode, 
grows  rapidly  into  a  brilliant  bull's-eye.  The 
appearance  is  very  realistic,  for  if  now  resist- 
ance is  cut  in,  the  dark  space  around  the 
cathode  (as  is  evident  after  a  moment's  re- 
flection) grows  smaller,  and  vice  versa.  Its 


FIG.  2. 

outline  is  exceedingly  sharp  and  perfectly 
steady,  and  yet,  though  the  discharge  appears 
very  brilliant,  the  current  required  may  not 
exceed  20  milliamperes. 

This  form  of  discharge  vessel  offers  an  in- 
teresting method  for  the  study  of  the  stria- 
tions  and  their  relative  spacing  with  reference 
to  the  impressed  discharge  potentials.  These 
effects  are  best  shown  when  the  vacuum  is  not 
too  high  and  the  discharge  potential  is  ad- 
justed to  give  a  patch  on  the  cathode,  which 
we  will  take  as  the  inner  cylinder,  of  about 
one  square  centimeter  in  area.  Under  these 
conditions  the  Faraday  dark  space  should  be 
about  8  mm.  in  length,  and  the  Crookes  dark 
space  should  be  just  visible  between  the  vel- 
vety cathode  glow  and  the  cathode  electrode. 


Another  prerequisite  is  that  the  discharge 
must  not  cling  to  the  edge  of  the  aluminum 
electrodes,  but  should  occupy  some  intermedi- 
ate position  as  shown  at  1  in  a,  Fig.  1.  In  this 
position  the  characteristics  of  the  discharge 
are  shown  with  exceeding  clearness.  If  now 
some  additional  resistance  is  cut  in,  the  area 
of  the  discharge  will  become  less,  the  Fara- 
day dark  space  will  shorten,  the  positive  col- 
umn will  move  towards  the  cathode,  and  the 
number  of  striae  in  it  will  increase,  the  extra 
striae  being,  as  it  were,  drawn  out  of  the  anode. 
The  configuration  is  perfectly  steady  except 
that  the  discharge,  as  a  whole,  is  liable  to 
wander.  This  transition  may  be  continued  by 
a  still  further  increase  of  the  resistance  in  the 
circuit,  the  dark  space  becoming  ever  shorter, 
the  positive  column  lengthening  and  at  the 
same  time  shrinking  in  area  and  the  stria?  in- 
creasing in  number,  all  without  loss  of  out- 
line or  brightness.  Finally,  the  discharge  will 
cease.  The  various  stages  are  suggested  at  1, 
2,  3  in  lf  Fig.  1. 

In  the  second  method  the  discharge  vessel 
with  its  commutator  is  placed  in  a  derived 
circuit  (Fig.  2).  This  arrangement  enables  the 
discharge  potential  to  be  continuously  varied 
over  a  wide  range,  and  hence  for  a  given 
vacuum  the  relation  between  the  length  of  the 
dark  space  and  the  impressed  voltage  may  be 
exhibited.  Again  this  arrangement  enables 
the  minimum  potential  to  be  readily  deter- 
mined that  will  maintain  a  discharge.  As  an 
example,  for  a  given  vacuum  with  the  resist- 
ance AC  equal  to  1/3  that  of  AB  the  discharge 
was  observed  to  just  pass,  indicating  that  the 
potential  necessary  was  330  volts. 

Additional  phases  of  the  experiment  will 
suggest  themselves  to  the  operator. 

CHAS.  T.  KNIPP 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
March  4,  1916 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  VII,  No.  6,  June,  1916.] 


RETROGRADE  RAYS  FROM  THE  COLD  CATHODE. 

BY  ORRIN  H.  SMITH. 

JJ.  THOMSON,1  as  early  as  1897,  showed  that  a  system  of  rays  of 
•  an  entirely  different  character  from  the  cathode  rays  accompanies 
the  cathode  beam.  He  found  that  these  rays  proceed  normally  from 
the  face  of  the  cathode,  that  they  are  not  appreciably  deflected  by  a 
permanent  magnet,  and  that  they  possess  very  little,  if  any,  power  of 
producing  phosphorescence. 

In  1906  Villard2  gave  an  account  before  the  French  Academy  of  the 
rays  accompanying  the  cathode  beam  which  are  not  so  readily  deflected 
as  the  cathode  beam  but  which  were  deflected  in  such  a  direction  and 
by  such  an  amount  as  would  be  expected  of  the  "kanal  strahlen."  He 
noticed  that  in  a  mixture  of  oxygen  and  hydrogen  (or  water  vapor)  the 
cathode  rays  produced  a  luminescence  characteristic  of  oxygen,  but  when 
these  were  deflected  aside  by  a  magnet  there  remained  rays  which  pro- 
duced a  luminescence  characteristic  of  hydrogen.  He  explained  their 
presence  by  saying  that  they  were  the  positive  canal  rays  which  fall 
against  the  cathode  and  rebound.  To  explain  their  rebounding  beyond 
the  limits  of  the  cathode  dark  space,  he  assumed  that  the  potential  fall 
underwent  rapid  variations  or  was  even  discontinuous.  A  stroboscopic 
test  showed  this  to  be  true;  however,  this  was  to  be  expected  since  he 
used  a  transformer  to  produce  the  discharge. 

The  following  year  Thomson3  showed,  independently,  that  these  rays 
were  deflected  by  strong  electric  and  magnetic  fields  and  that  they 
possessed  considerable  mass.  In  a  later  work  he  observed  that  they 
were  very  feeble  under  the  most  favorable  conditions  of  vacuum,  dis- 
charge potential,  etc.,  and  were  exceedingly  feeble  when  the  gas  pressure 
in  the  discharge  tube  was  very  low.  In  this  latter  respect  they  were 
quite  different  from  canal  or  positive  rays.  Employing  a  tube  having 
an  opening  of  about  .5  mm.  in  diameter  he  obtained  a  photograph  which 
showed  that  these  rays  contain  (a)  positively  electrified  atoms  and  mole- 
cules of  hydrogen,  (b)  positively  electrified  atoms  of  oxygen,  and  (c) 
negatively  electrified  atoms  of  hydrogen  and  oxygen.  The  photograph 

1  Proc.  Camb.  Phil.  Soc.,  IX.,  p.  243,  1897. 
1  Comptes  Rendus,  CXLIIL,  p.  673,  1906. 
*  Phil.  Mag.,  XIV.,  p.  359,  1907. 


626 


ORRIN  H.  SMITH. 


[SECOND 

[SERIES. 


showed  the  intensity  of  the  lines  corresponding  to  the  negative  ions  to 
be  greater  than  that  of  the  positive  ions.  With  the  ordinary  positive 
rays  the  positive  lines  are  the  more  intense. 

The  conditions  under  which  retrograde  rays  are  produced  are  quite 
different  from  those  that  obtain  for  the  ordinary  positive  rays  and  for 
this  reason  it  seemed  worth  while  to  repeat  and  extend  Thomson's 
investigations. 

Thomson  does  not  find  the  molecule  of  oxygen  with  the  negative 
charge  while  in  this  investigation  the  molecule  of  oxygen  and  the  molecule 
of  hydrogen  are  the  only  carriers  obtained  with  a  negative  charge,  no 
atoms  appearing  at  all.  The  presence  of  helium  in  the  discharge  chamber 
apparently  makes  no  difference  in  the  photographic  result. 


Fig.  1. 

Top  View.  MN,  containing  vessel  ot  glass;  pp,  glass  end  plates;  mn,  large  brass  cylinder; 
m'nr,  magnetic  field  extensions;  EE,  electrostatic  field  plates,  connections  to  which  are  not 
shown;  m"n",  plateholder;  P,  photographic  plate  mounted  on  disc  d,  supported  by  telescoping 
cap  m'"n"' ,  and  turned  by  winch  w,  DD,  aluminum  diaphragms;  and  SI.  iron  shield. 

It  appears  that  Thomson  was  unable  to  use  a  tube  of  less  than  .5  mm. 
bore,  while  in  this  investigation  traces  were  obtained  with  a  tube  and 
set  of  diaphragms  having  openings  of  about  .05  mm.  thus  producing 
sharp  lines  on  the  plate  which  made  possible  more  accurate  measurements. 

Owing  to  the  short  range  at  which  these  rays  were  obtained  on  the 
photographic  plate,  the  increased  sharpness  of  the  lines,  and  the  re- 
stricted range  of  their  velocities  due  to  a  restricted  cathode  dark  space, 
it  was  possible  to  obtain  some  evidence  on  the  question  as  to  whether 
the  power  of  a  particle  to  affect  a  photographic  plate  is  a  function  of  its 


NoL6VIL]  RETROGRADE  RAYS  FROM  THE  COLD  CATHODE.  62  J 

velocity,  momentum,  or  kinetic  energy.  This  evidence  seems  to  indicate 
that  it  is  a  function  of  the  kinetic  energy  and  that  the  mean  value  is 
about  7.4  X  io~9  ergs. 

The  apparatus,  shown  in  Fig.  I,  and  the  manipulation  is  essentially 
the  same  as  that  described  by  Knipp1  except  that  a  cold  cathode  was  used 
instead  of  the  Wehnelt  cathode  and  the  discharge  was  produced  by  an 
induction  coil.  The  cathode  was  just  like  the  anode  and  similarly  placed 
facing  the  line  of  the  tube  and  the  diaphragms. 

A  large  Leeds  induction  coil  was  operated  on  ten  storage  cells.  The 
vacuum  was  maintained  with  the  aid  of  a  large  charcoal  bulb  dipping 
into  liquid  air.  In  general  the  vacuum  improved  with  sparking.  After 
a  few  runs  it  was  found  that  the  liquid  air  could  be  removed  after  about 
ten  minutes  from  starting,  and,  as  the  sparking  and  pumping  continued, 
it  co aid  be  dispensed  with  altogether.  Finally  the  vacuum  was  so  easily 
maintained  that  it  was  necessary  to  keep  the  pump  itself  turned  off  for 
about  three  fourths  of  the  time. 

There  is  a  point  of  interest  in  connection  with  the  charcoal  bulb.  It 
was  left  on  the  apparatus  for  weeks  after  its  use  was  found  unnecessary, 
remaining  all  the  while  at  the  nearly  constant  room  temperature.  The 
pumps  were  unable  to  produce  a  vacuum  of  .005  mm.  in  fully  three 
hours'  time  when  starting  from  atmospheric  pressure,  and  this  was  the 
case  whether  the  bulb  was  heated  for  an  hour  during  that  time  or  not. 
However,  if  it  was  pumped  to  a  pressure  of  one  or  two  mm.  and  left  to 
stand  for  ten  to  fifteen  hours  then  upon  starting  the  pumps  a  vacuum  of 
.005  mm.  could  be  attained  in  twenty  to  thirty  minutes.  This,  strangely, 
was  true  even  when  the  vacuum  had  been  let  down  for  a  very  few  minutes 
and  then  the  pumps  started  again  immediately. 

The  photographic  plate  used  was  Seed's  Yellow  Label  lantern  slide 
plate.  This  plate  is  very  slow  and  hence  produces  great  contrast  which 
is  the  thing  desired.  Thomson2  points  out  that  the  large  ions  affect 
only  the  surface  of  the  film  and  do  not  penetrate  like  the  faster  moving 
electrons,  into  the  film.  Hence  the  plate  best  suited  for  this  work  is  one 
that  is  slow  and  that  has  a  thin  film  with  a  high  percentage  of  silver. 
The  best  traces  that  could  be  gotten  in  this  investigation  were  in  many 
instances  so  thin  that  they  could  hardly  be  seen.  They  were  obscured 
easily  by  the  slightest  fogging.  For  this  reason  a  fast  plate  could  not  be 
used.  Seed's  Gilt  Edge  Number  Twenty-seven  plate  was  tried  but  in 
every  instance  fogging  obscured  the  lines.  The  Double  Coated  Cramer 
Crown  plate  was  tried  and  found  to  be  entirely  too  sensitive.  Some 

1  PHYS.  REV.,  XXXIV.,  p.  215,  March,  1912. 

2  Thomson,  Rays  of  Positive  Electricity,  p.  4. 


628  ORRIN  H.  SMITH. 

experience  by  another  member  of  the  department  obviated  the  necessity 
of  trying  the  Cramer  X-ray  plate.  As  an  instance  to  show  that  these 
carriers  affect  only  the  surface  of  the  film,  the  author  gently  stroked  the 
film  under  water  with  a  fine  camel's  hair  brush  to  remove  foreign  particles 
and  it  was  found  that,  in  some  cases,  the  lines  were  entirely  obliterated. 
Further,  after  the  negative  had  dried  the  lines  could  be  obliterated  by 
breathing  on  the  film  and  wiping  it  gently  with  a  soft  cloth.  In  both 
cases,  other  than  erasing  the  lines,  no  further  change  could  be  detected 
in  the  film.  It  was  found  advantageous  to  put  some  alum  in  the  fixing 
bath  to  harden  the  film.  The  developer  used  was  ordinary  hydrochinon, 
the  time  of  development  being  from  six  to  twelve  minutes. 

The  time  of  exposure  varied  from  thirty  minutes  for  the  small  to  three 
hours  for  the  larger  deflections.  There  seems  to  be  a  limit  to  the  intensity 
that  is  obtainable,  for  after  a  certain  length  of  exposure  the  intensity 
of  the  lines  did  not  apparently  increase  with  further  exposure.  This 
was  true  for  long  or  short  development  or  even  when  they  were  exceed- 
ingly dim.  This  is  in  agreement,  however,  with  the  theory  that  they 
affect  only  the  surface  of  the  film. 

Thomson  found  that  the  retrograde  rays  were  best  obtained  when  the 
gas  pressure  was  not  too  low.  The  present  photographs  bear  out  that 
fact  very  well.  If  the  vacuum  was  kept  about  .002  to  .004  mm.  scarcely 
any  trace  of  the  rays  could  be  found  on  the  plate.  The  best  pressure  for 
their  production  seems,  from  this  investigation,  to  be  between  .015  and 
.008  mm. 

There  is  always  a  central  spot  that  is  undeflected  which  is  probably 
due  to  neutral  carriers  that  were  negative  originally  but  which  lost  one 
electron  before  they  got  into  the  deflecting  fields.  It  would  seem  from 
this  that  a  moving  particle  need  not  be  charged  in  order  to  affect  a  photo- 
graphic plate.  It  is  quite  evident  that  the  velocity  of  an  uncharged 
particle  must  be  above  a  certain  value  otherwise  a  plate  would  be 
affected  by  exposure  to  the  air  in  a  dark  room  due  to  no  other  agency 
than  to  the  velocity  of  the  air  molecules  produced  by  ordinary  heat 
agitation.  The  mean  of  this  velocity  at  o°  C.  for  the  hydrogen  molecule 
is  about  2  X  io5  cm./sec.  and  for  the  oxygen  molecule  about  4.5  X  io4 
cm./sec.  Whether  the  ability  of  a  moving  particle  to  affect  a  photo- 
graphic plate  is  due  to  its  momentum  or  its  kinetic  energy,  or  simply  to 
its  velocity,  is  not  definitely  known.  It  seems  reasonable  to  expect, 
however,  that  it  should  be  a  function  of  one  of  these.  On  a  number  of 
the  plates  the  lines  were  distinct  enough  to  locate  approximately  the 
place  where  the  slowest  ions  would  strike,  i.  e.,  those  that  had  just  suffi- 
cient velocity  to  affect  the  plate.  These  points  were  found,  in  every 


VOL.  VII.1 
No.  6. 


RETROGRADE  RAYS  FROM  THE  COLD  CATHODE. 


629 


case,  to  be  well  within  the  limits  of  the  field,  i.  e.,  so  far  as  the  limits  of 
the  apparatus  are  concerned  the  lines  might  have  extended  farther  from 
the  origin.  It  occurred  to  the  author  then  to  assume  that  there  were 
particles  which  struck  beyond  the  last  points  of  the  visible  trace  but  whose 
velocity  was  not  sufficient  to  cause  them  to  affect  the  film.  If  the 
coordinates  of  the  last  visible  point  in  each  line  be  measured  and  v  and 
e/m  determined,  then,  for  all  such  points,  we  should  get  a  constant, 
showing  whether  this  minimum  effect  on  the  plate  is  a  function  of  the 
velocity,  the  momentum,  or  of  the  kinetic  energy  of  the  moving  ion. 
Table  I.  shows  values  which  are  proportional  to  the  velocity,  momentum, 
and  kinetic  energy  for  the  points  in  question  on  sixteen  different  lines. 
It  can  be  seen  that  the  values  for  the  kinetic  energy  are  nearly  constant 
while  the  values  for  the  velocity  and  the  momentum  are  not  constant. 
It  thus  appears  that  the  power  of  a  particle  to  affect  a  photographic 
film  probably  depends  on  its  kinetic  energy.  The  mean  of  these  values 
of  the  kinetic  energy  is,  from  Table  I.,  7.4  X  io~9  ergs  which  is  the 
minimum  required.  This  value  would  probably  be  different  for  an 
electron  because  of  its  size.  It  is  somewhat  larger  than  the  energy  re- 
quired to  produce  an  ion  which  is  1.63  X  io~u  ergs.  The  above  value 
(7.4  X  io~9)  was  calculated  from  data  obtained  from  this  investigation, 
except  for  the  value  of  e,  by  the  formula 

kinetic  energy  =  i/2-m/e-e-v2. 


-20 


The  value  of  e  was  taken  as  1.55  X  10 


TABLE  I. 


Photographic 
Plate. 

Line. 

Constant  X 
Velocity. 

Constant  X 
Momentum. 

Constant  X 
Kinetic  Energy. 

75 

Upper 

6.04 

18.36 

111.0 

76 

Upper 

6.54 

17.99 

117.6 

76 

Lower 

1.36 

87.18 

118.6 

85 

Upper 

6.37 

12.50 

79.0 

85 

Lower 

1.52 

52.50 

79.7 

86 

Upper 

6.23 

12.71 

79.2 

86 

Lower 

1.53 

52.48 

80.4 

87 

Upper 

7.27 

19.40 

102.5 

87 

Lower 

1.69 

60.50 

102.3 

88 

Lower 

1.37 

61.70 

84.5 

94 

Upper 

5.55 

10.71 

106.4 

94 

Lower 

1.77 

36.28 

100.4 

95 

Upper 

7.41 

15.03 

91.1 

95 

Lower 

1.64 

51.50 

84.47 

96 

Upper 

6.35 

17.70 

112.5 

96 

Lower 

1.42 

59.36 

84.26 

630  ORRIN  H.  SMITH. 

It  can  be  seen  from  Table  I.  that,  even  though  the  values  of  the  kinetic 
energy  vary  somewhat,  the  values  for  a  given  plate  as  a  rule  are  more 
nearly  alike.  Plate  ninety-six  furnishes  the  greatest  variation  from  this 
rule.  It  might  be  reasonable  to  expect  that  different  emulsion  numbers 
would  reveal  slightly  different  kinetic  energies  required  to  affect  the  film. 
Several  emulsion  numbers  are  represented  in  these  data. 

The  photographs  taken  with  the  apparatus  in  the  last  refinement, 
while  clear  and  capable  of  accurate  measurement,  do  not  lend  themselves 
to  reproduction  and  hence  are  omitted.  The  important  dimensions  are 
as  follows: 

Length  of  electrostatic  field 1.10  cm. 

Length  of  magnetic  field 1.10  cm. 

Distance  from  point  of  emergence  to  plate 1.58  cm. 

Length  of  triangular  test  coil1 2.52  cm. 

Base 63  cm. 

Number  of  turns 19. 

The  negative  lines  show  distinctly  the  parabolic  heads  which  are  not 
in  evidence  on  the  positive  lines.  It  was  evident  from  nearly  all  the 
plates  exposed  that  the  negative  carriers  are  in  preponderance  over  the 
positive  ones.  This  seems  reasonable  to  expect  since  the  distance  to 
the  plate  is,  for  the  lower  pressures,  within  the  limits  of  the  mean  free 
path  and  it  is  necessary  to  assume  that  every  positive  carrier  has  lost 
two  electrons  between  the  outer  limits  of  the  dark  space  and  the  deflecting 
fields.  If  this  is  true  we  should  expect  that  the  lines  due  to  the  positive 
carriers  would  not  be  as  sharp  as  those  due  to  the  negative  carriers, 
the  ions  being  deflected  somewhat  from  their  true  path  in  the  process 
of  losing  an  electron.  Most  of  the  photographs  bear  this  out.  It  is 
somewhat  surprising,  in  consideration  of  the  foregoing,  that  this  pre- 
ponderance is  not  greater  than  the  photographs  seem  to  indicate  unless 
the  negative  ion  is  more  unstable  than  the  positive  ion.  An  additional 
suggestion  in  the  same  line  comes  from  a  study  of  Thomson's  photographs 
of  positive  rays,  in  a  great  many  of  which  the  negative  counterpart  is 
very  weak  or  cannot  be  seen  at  all  on  the  prints  when  the  positive  lines 
are  very  pronounced.  The  positive  lines  do  not  have  the  distinct  para- 
bolic head  that  the  negative  lines  have.  They  are  also  broader  and 
more  diffuse.  Joining  the  parabolic  head  to  the  center  is  a  line  due  to 
the  secondary  rays  of  Thomson.  This  is  shown  particularly  in  one 
exposure  where  the  electric  field  overlapped  the  magnetic  so  that  the 
secondary  line  does  not  join  straight  on  to  the  head  of  the  parabola. 
The  data  for  exposure  number  eighty-five,  are  given  in  Table  II.  This 

1  Thomson,  Rays  of  Positive  Electricity,  p.  10. 


VOL.  VII.l 
No.  6. 


RETROGRADE  RAYS  FROM  THE  COLD  CATHODE. 


631 


indicates  that  the  carriers  which  produced  the  two  lines  are  the  mole- 
cules of  hydrogen  and  oxygen  respectively.  The  measurements  of  the 
coordinates  were  made  with  an  ordinator  composed  of  a  frame  to  which 
the  plates  could  be  fastened  so  that  there  was  a  movable  point  above  the 
plate  capable  of  being  carried  in  either  of  two  directions  perpendicular  to 
each  other  by  micrometer  screws.  A  Grassot  fluxmeter  was  used  to 
determine  the  strength  of  the  magnetic  field. 

TABLE  II. 

Photographic  Plate  Number  85. 
Measurements  for  the  Upper  Line. 


Position. 

z  in  mm. 

y  in  mm. 

v  X  io-» 
cm./sec. 

elm  X  1Q"4 

Electric 
Atomic 
Weight. 

Carrier. 

1 

3.34 

6.42 

6.37 

.509 

1.97 

H2 

2 

2.46 

5.48 

7.39 

.504 

1.99 

" 

3 

1.88 

4.77 

8.96 

.500 

2.00 

14 

4 

1.12 

3.51 

10.38 

.458 

2.18 

M 

Measurements  for  the  Lower  Line. 


1 

3.34 

1.53 

1.52 

.029 

34.5 

03 

2 

2.46 

1.31 

1.77 

.0288 

34.8 

H 

3 

1.88 

1.16 

2.04 

.0296 

33.8 

" 

4 

1.12 

.84 

2.50 

.0260 

38.5 

« 

Time  of  exposure,  3.25  hours. 

Gas  pressure  varied  between  .008  and  .018  mm. 

Electric  deflecting  field,  965  volts. 

Magnet  current,  4.25  amperes. 

A  =  8,040,  B  =267  X  109 

All  the  photographs  were  exposed  with  residual  air  in  the  discharge 
chamber  except  number  88.  In  this  instance  it  contained  some  helium 
but  no  traces  appear  in  the  photograph,  in  fact  in  no  case  does  anything 
appear  in  any  of  the  photographs  except  the  lines  due  to  the  molecules 
of  hydrogen  and  oxygen.  In  some  cases  the  positive  rays  are  not  visible. 

The  data  show  very  well  how  the  velocity  varies  for  the  carriers 
striking  at  the  various  points  along  the  parabola,  that  it  decreases 
with  increase  of  distance  from  the  undeflected  spot.  The  value  of  v 
and  elm  obtained  for  the  smaller  values  of  the  electric  field  are  in  general 
less  reliable  than  for  those  for  which  the  deflection  is  larger.  The  "elec- 
tric atomic  weight"  of  a  carrier  Thomson1  has  defined  as  the  ratio  of 
m/e  for  that  carrier  to  m/e  for  the  atom  of  hydrogen. 

1  Phil.  Mag.,  XXI.,  p.  234,  Feb.,  1911. 


632  ORRIN  H.  SMITH. 

It  was  noticed  in  connection  with  these  experiments  that  the  dis- 
charge in  the  chamber  passed  more  easily  with  the  presence  of  a  transverse 
magnetic  field.  Earhart1  has  shown  that  this  is  true  for  a  longitudinal 
field. 

SUMMARY  OF  CONCLUSIONS. 

The  results  of  this  investigation  may  be  summarized  briefly  as  follows : 

1.  When  obtaining  retrograde  rays  in  residual  air  the  molecule  of 
hydrogen  appears  on  every  plate  accompanied  by  a  heavier  carrier  which 
in  most  cases  is  the  molecule  of  oxygen.     The  velocities  obtained  by  the 
author  are  smaller  than  those  obtained  by  Thomson.     This  is  due  to  the 
position  of  the  cathode  with  reference  to  the  small  canal  through  which 
the  carriers  pass,  the  dark  space  extending  beyond  the  near  end  of  this 
tube  and  hence  the  carriers  not  attaining  their  maximum  velocity. 

2.  The  negative  lines  are  clearer  and  sharper  than  the  positive;  prob- 
ably because  of  the  disturbance  to  the  path  of  the  positive  particles  in 
the  process  of  becoming  positive. 

3.  Retrograde  rays  can  be  obtained  with  a  canal  having  a  bore  of 
about  .05  mm.  diameter.     The  best  range  of  pressures  for  their  production 
is  between  .008  and  .015  mm.  of  mercury. 

4.  The  power  of  a  moving  particle  to  affect  a  photographic  plate  seems 
to  be  a  function  of  its  kinetic  energy.     The  minimum  required  for  the 
heavy  carriers  is  of  the  order  7.4  X  io~9  ergs,  which  is  larger  than  the 
energy  required  to  produce  an  ion,  however,  there  is  evidence  in  favor  of 
the  view  that  this  value  may  depend  somewhat  on  the  emulsion  on  the 
plate. 

In  conclusion  I  wish  to  express  my  thanks  to  Professor  A.  P.  Carman 
for  the  excellent  facilities  placed  at  my  disposal  and  to  Dr.  C.  T.  Knipp 
for  his  interest  and  help  in  carrying  on  the  investigation. 
LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS. 

1  PHYS.  REV.,  Feb.,  1914. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  VIII,  No.  i,  July,  1916.  J 


AN  EXPERIMENTAL  VERIFICATION  OF  THE  LAW  OF  VARI- 
ATION OF  MASS  WITH  VELOCITY  FOR  CATHODE 

RAYS. 

BY  LLOYD  T.  JONES. 

INTRODUCTION. 

HHE  mass  of  the  electron  has  been  shown  by  W.  Kaufmann1  to  be 
-*-  electromagnetic  in  origin.  This  mass  is  shown  by  the  elementary 
laws  of  electromagnetism  to  be  constant  for  small  velocities  of  the  elec- 
tron. M.  Abraham2  has  developed  an  electro-dynamic  theory  of  moving 
electrons  by  which  he  accounts  for  the  falling  off  of  the  ratio  e/m  for 
electrons  moving  with  high  velocities.  If  /3  is  the  ratio  of  the  velocity 
of  the  electron  to  that  of  light,  the  ratio  of  the  mass  of  the  electron  moving 
with  the  velocity  v  to  its  mass,  mo,  when  moving  with  a  slow  velocity  is 

m        i 


The  Lorentz-Einstein  formula,  which  satisfies  the  principle  of  relativity, 
gives  the  ratio  of  the  masses  as 


Kunz3  has  discussed  the  bearing  of  these  formulae  in  connection  with 
an  electromagnetic  emission  theory  of  light  and  has  developed  three 
forms  of  the  formula  based  on  possible  changes  of  form  of  the  electron. 

Stark4  has  found  that  the  mass  of  the  cathode  particle  increases  as  the 
velocity  increases.  The  maximum  velocity  employed  by  him,  I.I4XIO10 
cm.  per  sec.,  was,  however,  not  great  enough  to  cause  more  than  a  small 
per  cent,  increase  in  the  mass. 

Later  Guye  and  Ratnsoky5  carried  out  an  experiment  employing  rays 
of  14.7  X  io10  cm.  per  sec.  velocity  and  obtained  an  increase  of  nearly 
twenty  per  cent,  in  the  mass. 

Each  of  the  investigators  has  employed  a  method  in  which  the  cathode 

1  W.  Kaufmann,  Gott.  Nachr.,  1901,  Heft  2;  1902,  Heft  5;  Phys.  Zeitschr.,  4,  54,  1902. 

2  M.  Abraham,  Gott.  Nachr.,  1902,  Heft.  i. 

8  J.  Kunz,  Arch,  des  ScL,  Jan.  1913;  PHYS.  REV.,  p.  464,  1914. 
4  H.  Stark,  Verh.  d.  Deut,  Phys.  Gesell.,  5,  p.  241,  1903. 

6  Guye  and  Ratnosky,  Arch,  des  Sci.,  31,  p.  293,  1911.  Guye  and  Lavanchy,  Comptes 
Rendus,  p.  52,  July,  1915. 


53 


LLOYD  T.  JONES. 


[SECOND 

[SERIES. 


beam  traverses  nonuniform  electric  and  magnetic  fields  and  the  deflection 
is  shown  on  a  phosphorescent  screen  placed  perpendicular  to  the  path. 
This  necessitated  a  homogeneous  cathode  beam. 

The  conclusions  of  the  experimenter  must  be  based  on  a  large  number 
of  observations  taken  at  each  of  a  number  of  different  velocities.  The 
method  that  has  been  developed  for  the  present  research  lessens  materially 
the  difficulties  encountered  in  a  verification  by  cathode  rays  and  is 
applicable  equally  well  for  the  /3  particles  of  radium.  Perhaps  the  best 
feature  of  the  method  is  that  it  is  desired  to  have  rays  of  all  possible 
velocities  present  in  the  discharge  rather  than  a  homogeneous  beam. 
This  allows  one  to  use  the  discharge  from  a  high  potential  transformer 
without  any  additional  pieces  of  apparatus  to  operate  during  the  time 
of  exposure.  Since  from  a  single  photograph  calculations  may  be  made 
of  e/m  for  all  the  velocities  present  it  is  possible  to  obtain  the  desired 
results  by  a  single  exposure. 

THE  APPARATUS. 

In  a  previous  determination  of  e/m  and  v  for  cathode  rays1  an  apparatus 
was  used  involving  the  same  principles  as  this;  the  high  discharge  po- 
tentials used  in  the  present  investigation,  however,  necessitated  a  change 
in  the  manner  of  introducing  the  electrodes  and  more  effective  insulation 
guarding  against  the  ionizing  and  direct  effect  of  the  discharge. 


Fig.  1. 

A  glass  jar  11.5  cm.  in  diameter  and  about  35  cm.  long  had  a  2.2  cm. 
hole  bored  in  its  base  through  which  the  cathode  was  introduced.  The 
cathode  was  an  aluminum  disc  about  .8  cm.  in  diameter  carried  on  a 
small  brass  rod  encased  in  a  small  glass  tube  and  connected  with  one 
terminal  of  the  transformer  through  a  platinum  wire  sealed  in  the  glass. 


L.  T.  Jones,  PHYS.  REV.,  N.S.,  Vol.  III.,  p.  317.  19*4- 


No"iVI11']  VARIATION  OF  MASS  WITH  VELOCITY.  54 

The  glass  tube  encasing  the  cathode  rod  was  supported  at  two  places 
by  a  second  glass  tube  sealed,  as  shown  at  b  in  Fig.  I,  to  a  tube  of  2  cm. 
diameter  which  passed  through  the  hole  in  the  base  of  the  jar.  This 
tube  was  fastened  to  the  base  by  sealing  wax.  A  brass  cylinder,  C,  of 
10.2  cm.  diameter  and  about  32  cm.  long  was  fastened  rigidly  (manner 
not  shown)  to  the  glass  jar;  and  a  brass  ring,  R,  of  1.5  cm.  width  and  .4 
cm.  thickness  was  soldered  inside  it  with  its  plane  perpendicular  to  the 
axis  of  the  brass  cylinder.  An  iron  cylinder,  5,  of  7.5  cm.  inside  diameter 
and  .8  cm.  thickness  was  fastened  by  screws  to  the  ring  R.  An  ebonite 
ring,  Fj  of  nearly  the  same  dimensions  as  R  was  fastened  to  R  by  screws 
whose  heads  were  sunk  well  beneath  the  surface  next  G.  G  was  a  brass 
disc  of  .3  cm.  thickness  fastened  by  brass  screws  to  the  ebonite  disc,  L, 
which  was  of  .8  cm.  thickness  and  carried  the  electrostatic  plates. 
To  increase  the  insulation  discs  of  mica  were  placed  between  G  and  L, 
F  and  G  and  R  and  F.  To  prevent  trouble  due  to  the  heavy  discharge 
a  brass  disc,  M,  was  held  against  R  by  a  slip  ring  in  S.  A  few  millimeters' 
space  was  left  around  the  small  iron  tube,  /,  which  passed  through  di- 
rectly in  front  of  the  cathode. 

The  two  electrostatic  plates  were  brass  plates  20.5  X  7-5  X  1.2  cm. 
In  the  upper  one  was  inlaid  a  piece  of  soft  iron,  N,  5.13  X  1.4  X  .1  cm. 
A  similar  piece  of  iron,  P,  was  held  against  N  by  eight  short  iron  screws. 
After  the  iron  piece,  N,  was  inlaid  and  all  necessary  holes  had  been  made 
in  the  plates  they  were  annealed  and  then  one  side  of  each  was  surfaced 
to  within  .001  cm.  of  plane.  The  slip  P  also  had  its  face  next  N  made 
plane.  A  scratch  of  about  .05  cm.  width  was  drawn  full  length  on  the 
plane  side  of  P.  The  ends  of  this  scratch,  for  about  I  mm.  of  their 
length,  were  closed  with  solder  and  the  solder  cut  off  flush  with  the  sur- 
face. A  small  cut  was  then  made  in  each  of  the  bits  of  solder  and  these 
cuts  determined  the  path  of  the  electron  immediately  before  its  entrance 
into  the  deflecting  fields.  The  electron  then  takes  the  path  indicated 
by  the  dotted  line  in  Fig.  I.  The  electron  is  thus  protected  from  the 
fields  until  it  leaves  the  constricting  canal.  Care  was  taken  that  the 
small  cut  marking  the  entrance  of  the  electron  in  the  fields  was  perfect 
to  the  ends  of  N  and  P  and  that  the  ends  of  N  and  P  were  exactly  even. 
As  a  final  precaution  a  small  bit  of  solder  was  placed  in  the  middle  of  the 
canal  as  well  and  a  small  cut  made  in  it.  This  insured  a  straight  beam 
through  the  tube.  Each  of  these  cuts  was  .01  cm.  in  width  and  of  about 
the  same  depth.  The  softest  iron  obtainable  was  used  throughout  and 
the  brass  was  free  of  magnetic  material. 

The  ebonite  disc,  L,  with  its  plate,  G,  was  held  against  the  ring,  F, 
by  four  heavy  brass  screws  threaded  into  R.  They  were  insulated 
from  G  by  an  air  space  of  about  2  mm. 


53 


LLOYD  T.  JONES. 


[SECOND 
LSERIES. 


beam  traverses  nonuniform  electric  and  magnetic  fields  and  the  deflection 
is  shown  on  a  phosphorescent  screen  placed  perpendicular  to  the  path. 
This  necessitated  a  homogeneous  cathode  beam. 

The  conclusions  of  the  experimenter  must  be  based  on  a  large  number 
of  observations  taken  at  each  of  a  number  of  different  velocities.  The 
method  that  has  been  developed  for  the  present  research  lessens  materially 
the  difficulties  encountered  in  a  verification  by  cathode  rays  and  is 
applicable  equally  well  for  the  /3  particles  of  radium.  Perhaps  the  best 
feature  of  the  method  is  that  it  is  desired  to  have  rays  of  all  possible 
velocities  present  in  the  discharge  rather  than  a  homogeneous  beam. 
This  allows  one  to  use  the  discharge  from  a  high  potential  transformer 
without  any  additional  pieces  of  apparatus  to  operate  during  the  time 
of  exposure.  Since  from  a  single  photograph  calculations  may  be  made 
of  e/m  for  all  the  velocities  present  it  is  possible  to  obtain  the  desired 
results  by  a  single  exposure. 

THE  APPARATUS. 

In  a  previous  determination  of  e/m  and  v  for  cathode  rays1  an  apparatus 
was  used  involving  the  same  principles  as  this;  the  high  discharge  po- 
tentials used  in  the  present  investigation,  however,  necessitated  a  change 
in  the  manner  of  introducing  the  electrodes  and  more  effective  insulation 
guarding  against  the  ionizing  and  direct  effect  of  the  discharge. 


Fig.  1. 

A  glass  jar  11.5  cm.  in  diameter  and  about  35  cm.  long  had  a  2.2  cm. 
hole  bored  in  its  base  through  which  the  cathode  was  introduced.  The 
cathode  was  an  aluminum  disc  about  .8  cm.  in  diameter  carried  on  a 
small  brass  rod  encased  in  a  small  glass  tube  and  connected  with  one 
terminal  of  the  transformer  through  a  platinum  wire  sealed  in  the  glass. 

1  L.  T.  Jones,  PHYS.  REV.,  N.S.,  Vol.  III.,  p.  317,  1914. 


NoTiY111']  VARIATION  OF  MASS  WITH  VELOCITY.  54 

The  glass  tube  encasing  the  cathode  rod  was  supported  at  two  places 
by  a  second  glass  tube  sealed,  as  shown  at  b  in  Fig.  I,  to  a  tube  of  2  cm. 
diameter  which  passed  through  the  hole  in  the  base  of  the  jar.  This 
tube  was  fastened  to  the  base  by  sealing  wax.  A  brass  cylinder,  C,  of 
10.2  cm.  diameter  and  about  32  cm.  long  was  fastened  rigidly  (manner 
not  shown)  to  the  glass  jar;  and  a  brass  ring,  R,  of  1.5  cm.  width  and  .4 
cm.  thickness  was  soldered  inside  it  with  its  plane  perpendicular  to  the 
axis  of  the  brass  cylinder.  An  iron  cylinder,  6",  of  7.5  cm.  inside  diameter 
and  .8  cm.  thickness  was  fastened  by  screws  to  the  ring  R.  An  ebonite 
ring,  Fj  of  nearly  the  same  dimensions  as  R  was  fastened  to  R  by  screws 
whose  heads  were  sunk  well  beneath  the  surface  next  G.  G  was  a  brass 
disc  of  .3  cm.  thickness  fastened  by  brass  screws  to  the  ebonite  disc,  L, 
which  was  of  .8  cm.  thickness  and  carried  the  electrostatic  plates. 
To  increase  the  insulation  discs  of  mica  were  placed  between  G  and  L, 
F  and  G  and  R  and  F.  To  prevent  trouble  due  to  the  heavy  discharge 
a  brass  disc,  M ,  was  held  against  R  by  a  slip  ring  in  S.  A  few  millimeters' 
space  was  left  around  the  small  iron  tube,  /,  which  passed  through  di- 
rectly in  front  of  the  cathode. 

The  two  electrostatic  plates  were  brass  plates  20.5  X  7.5  X  1.2  cm. 
In  the  upper  one  was  inlaid  a  piece  of  soft  iron,  N,  5.13  X  1.4  X  .1  cm. 
A  similar  piece  of  iron,  P,  was  held  against  N  by  eight  short  iron  screws. 
After  the  iron  piece,  N,  was  inlaid  and  all  necessary  holes  had  been  made 
in  the  plates  they  were  annealed  and  then  one  side  of  each  was  surfaced 
to  within  .001  cm.  of  plane.  The  slip  P  also  had  its  face  next  N  made 
plane.  A  scratch  of  about  .05  cm.  width  was  drawn  full  length  on  the 
plane  side  of  P.  The  ends  of  this  scratch,  for  about  I  mm.  of  their 
length,  were  closed  with  solder  and  the  solder  cut  off  flush  with  the  sur- 
face. A  small  cut  was  then  made  in  each  of  the  bits  of  solder  and  these 
cuts  determined  the  path  of  the  electron  immediately  before  its  entrance 
into  the  deflecting  fields.  The  electron  then  takes  the  path  indicated 
by  the  dotted  line  in  Fig.  I.  The  electron  is  thus  protected  from  the 
fields  until  it  leaves  the  constricting  canal.  Care  was  taken  that  the 
small  cut  marking  the  entrance  of  the  electron  in  the  fields  was  perfect 
to  the  ends  of  N  and  P  and  that  the  ends  of  N  and  P  were  exactly  even. 
As  a  final  precaution  a  small  bit  of  solder  was  placed  in  the  middle  of  the 
canal  as  well  and  a  small  cut  made  in  it.  This  insured  a  straight  beam 
through  the  tube.  Each  of  these  cuts  was  .01  cm.  in  width  and  of  about 
the  same  depth.  The  softest  iron  obtainable  was  used  throughout  and 
the  brass  was  free  of  magnetic  material. 

The  ebonite  disc,  L,  with  its  plate,  G,  was  held  against  the  ring,  F, 
by  four  heavy  brass  screws  threaded  into  R.  They  were  insulated 
from  G  by  an  air  space  of  about  2  mm. 


55  LLOYD  T.  JONES. 

The  two  electrostatic  plates  were  held  at  a  fixed  distance  apart  by 
four  porcelain  blocks  placed  one  at  each  corner.  Under  the  back  end 
of  the  lower  plate  was  placed  a  brass  leg,  Q,  of  adjustable  height  which 
served  as  an  additional  support  for  the  plates  and  at  the  same  time  con- 
nected the  lower  plate  electrically  with  the  brass  cylinder,  and  through 
it  with  M  and  5. 

A  hole  2.2  cm.  in  diameter  was  bored  in  the  side  of  the  glass  jar  at  a 
suitable  position  and  a  glass  tube  waxed  to  the  jar  here  connected  the 
vessel  to  the  molecular  pump.  A  wire,  At  was  connected  to  the  brass 
cylinder  near  the  back  where  it  could  be  easily  reached  from  the  outside. 
A  was  connected  to  earth  and  to  the  second  terminal  of  the  transformer. 
The  surfaces  of  M  and  S  served  as  anode.  The  upper  of  the  electrostatic 
plates  was  connected  electrically  to  the  outside  by  a  wire,  B,  passing 
through  an  insulating  plug  in  the  brass  cylinder  and  through  a  small 
hole  in  the  glass  cylinder.  The  hole  was  made  vacuum  tight  by  sealing 
wax. 

The  photographic  chamber  was  made  light  tight  by  closing  the  ends 
of  the  cylinder  with  a  brass  cap  and  the  jar  was  made  vacuum  tight  by 
closing  with  a  glass  plate  sealed  on  with  a  mixture  of  beeswax  and  resin. 

The  electrostatic  potential  was  applied  to  A  and  B  and  the  transformer 
connected  to  A  and  D. 

THE  SPACING  BLOCKS. 

Each  of  the  four  spacing  blocks  placed  between  the  corners  of  the 
electrostatic  plates  was  a  length  of  a  porcelain  tube  of  1.2  cm.  external 
diameter.  After  the  sections  had  been  cut  from  the  tube  they  were  waxed 
inside  a  short  piece  of  brass  tubing  whose  outside  was  accurately  round 
so  it  could  be  chucked  in  the  grinding  machine.  They  were  ground  down 
till  they  were  of  nearly  the  same  length  and  the  end  planes  parallel. 
They  were  then  finished  by  hand  on  an  iron  plate  with  emery  till  they 
were  very  accurately  the  same  length  and  the  end  planes  parallel  as  the 
measurements  showed.  The  length  of  the  blocks  was  measured  by  an 
optical  lever  of  24.415  cm.  length  with  a  scale  3  meters  distant.  The 
lengths  of  the  blocks  were  .9822  ±  .0008  cm. 

THE  ELECTROSTATIC  POTENTIAL. 

A  high  potential  storage  battery,  T,  was  used  to  send  a  small  current 
through  two  high  resistances,  M  and  R,  shown  in  Fig,  2.  M  consisted  of 
two  Wolff  boxes  aggregating  2  X  io6  ohms  and  R  was  an  adjustable  resist- 
ance of  io4  ohms.  The  potential  drop  across  a  part  of  M  was  compared 
by  means  of  the  potentiometer,  P,  with  a  Weston  standard  cell  of  1.0183 
volts  at  24°  C.  The  standard  cell  checked  with  one  recently  received 


No^iY111']  VARIATION  OF  MASS  WITH  VELOCITY.  56 

from  the  Bureau  of  Standards.  By  adjusting  R  the  value  was  easily 
kept  constant  to  within  I  volt  and  the  value  thus  determined  to  less  than 
.1  per  cent.  The  two  electrostatic  plates  were  connected  directly  to  the 
terminals  of  M. 


Fig.  2. 

THE  MAGNETIC  FIELD. 

The  magnetic  field  was  due  to  a  constant  current  through  240  turns  of 
wire  wound  on  a  rectangular  wooden  frame  about  160  X  60  cm.  The 
cross-section  of  the  coil  of  wire  was  about  2X2  cm.  Calculation  showed 
the  field  to  be  uniform  over  a  range  greater  than  that  used. 

The  field  was  calibrated  by  the  aid  of  a  solenoid  of  1 ,141  turns  and  149.83 
cm.  length  wound  uniformly  on  a  wooden  frame  of  aboat  6X9  cm. 
cross-section.  The  solenoid  was  placed  in  the  geometrical  center  of  the 
rectangular  frame  so  that  the  fields  either  coincided  or  opposed  each 
other.  A  small  coil  of  about  200  turns  of  very  fine  wire  wound  on  an 
ebonite  rectangle  2X8  cm.  was  then  placed  in  the  center  of  the  solenoid. 
This  coil  was  connected  to  a  Grassot  fluxmeter  whose  scale  was  about  4 
meters  distant.  A  known  constant  current  was  sent  through  the  coil  to 
be  calibrated  and  the  current  through  the  solenoid  adjusted  until  the 
fluxmeter  showed  no  deflection  when  the  two  currents  were  broken 
simultaneously.  The  ratio  of  the  currents,  70  to  13.55,  gave  the  value 
of  the  field  to  be  1.854  gausses  per  ampere.  A  field  of  .002  gauss  pro- 
duced a  deflection  of  .3  mm.  on  the  fluxmeter  scale. 

THE  MEASUREMENT  OF  THE  CURRENT. 

The  current  in  the  magnetic  field  was  measured  with  a  Siemens  & 
Halske  ammeter  of  150  scale  divisions  which,  with  the  shunt  used,  had  a 
range  of  o  to  3  amperes.  The  ammeter  was  calibrated  by  passing  a  current 
through  it  in  series  with  two  Hartmann  &  Braun  standard  resistances  of 
.1  and  i  ohm.  The  potential  drop  across  each  resistance  was  measured 
by  the  Wolff  potentiometer  against  the  Weston  standard  cell  and  the 
current  calculated.  The  standard  resistances  were  kept  in  an  oil  bath 
at  constant  temperature.  The  Reichsanstalt  certificates  showed  the 
resistances  to  be  sufficiently  correct.  The  calibrations  by  the  two 
resistances  checked.  Throughout  the  calibrations  and  experiment  an 
adjustable  resistance  was  used  to  set  the  ammeter  needle  exactly  on  a 


57  LLOYD  T.  JONES.  [s££S 

scale  mark  in  order  that  any  variation  in  the  current  could  be  more 
easily  detected.  With  special  care  taken  for  good  contacts  little  dif- 
ficulty was  experienced  in  keeping  the  ammeter  needle  exactly  on  the 
division  mark. 

THE  VACUUM. 

The  Gaede  molecular  pump,  with  the  Gaede  mercury  pump  as  a  pre- 
liminary, was  used  for  the  exhaustion.  The  molecular  pump  was  con- 
nected by  30  mm.  tubing  directly  to  the  vessel  to  be  exhausted  with  no 
stopcock  or  other  constriction  intervening.  The  mercury  pump  was 
connected  to  a  McLeod  gauge  and  a  large  tube  of  cocoanut  charcoal. 
The  order  of  starting  the  pumps  assures  freedom  of  mercury  vapor  in 
the  discharge  tube.  The  construction  of  the  apparatus  with  its  sealing- 
wax  joints  made  it  quite  impossible  to  heat  the  vessel  to  rid  it  of  moisture. 
Such  a  proceeding  proved  unnecessary  with  the  wide  connecting  tubes 
used,  however,  as  an  hour  of  pumping  was  usually  sufficient  to  produce 
a  vacuum  that  caused  the  transformer  to  spark  20  cm.  between  its 
point  terminals  rather  than  pass  through  the  discharge  tube.  This 
degree  of  rarefaction  was  usually  produced  without  the  aid  of  liquid  air 
on  the  charcoal.  To  be  sure  the  equivalent  spark  length  of  the  tube 
always  dropped  a  few  centimeters  during  the  time  of  discharge,  but  a 
half  or  at  most  one  minute  of  pumping  was  sufficient  to  restore  the  vacuum. 

It  may  be  of  interest  to  some  users  of  the  molecular  pump  to  know 
that  considerable  trouble  was  experienced  with  the  pump  due  to  the 
creeping  in  of  oil  from  the  bearings.  Once  in  about  six  weeks  the  pump 
became  stiff  and  the  half  H.  P.  motor  was  unable  to  drive  it  at  the  normal 
speed  used,  8,000  R.  P.  M.  The  oil  was  then  taken  from  the  bearings 
and  the  whole  pump  thoroughly  washed  with  filtered  gasoline  and  dried 
by  drawing  air  through  it.  This  operation  usually  required  three  days, 

THE  ELECTRIC  DISCHARGE. 

The  transformer  used  to  produce  the  cathode  beam  was  one  built  for 
the  ratio  110-40,000  volts  operating  on  a  6o-cycle  circuit.  For  a  number 
of  photographs  it  was  used  on  a  44O-volt  6o-cycle  circuit.  The  rays 
thus  produced  were  of  rather  a  slow  velocity  although  the  vacuum  was 
so  high  that  the  transformer  sparked  across  a  20  cm.  gap  between  points 
outside.  In  order  to  lessen  the  amount  of  energy  used  and  still  retain 
the  potential  the  transformer  was  operated  on  no-volts  D.C.  with  a 
Wehnelt  interrupter.  This  arrangement,  with  or  without  a  capacity 
across  the  interrupter,  gave  rays  of  a  much  higher  velocity.  Under 
these  conditions,  however,  the  equivalent  spark  gap  of  the  vacuum  was 
only  about  8  to  12  cm. 


No" i y      ]  VARIATION  OF  MASS  WITH  VELOCITY.  58 

THE  FORMULA. 

The  beam  passes  through  uniform  electrostatic  and  magnetic  fields, 
whose  lines  are  parallel  to  each  other,  and  strikes  the  photographic 
plate  which  is  lying  on  the  lower  electrostatic  plate. 

Let  the  particle  be  subjected  to  the  simultaneous  action  of  the  electric 
and  magnetic  fields.  The  particle  will  be  bent  downward  by  the  electric 
field  and  strike  the  photographic  plate  at  a  distance  I  (measured  along 
the  direction  of  the  undeflected  beam)  from  the  source.  It  will  at  the 
same  time  be  bent  aside  by  the  magnetic  field  a  distance  z  (measured  at 
right  angles  to  Z) .  Since  many  velocities  are  present  they  will  show  them- 
selves in  a  long  trace  on  the  photographic  plate  and  e/m  may  be  calculated 
for  any  point  in  the  trace  and  hence  for  that  velocity.  If  the  electro- 
static field  alone  acts  the  resultant  trace  will  be  straight  down  the  center 
of  the  plate.  If  the  magnetic  field  also  acts,  then  for  each  value  of  the 
current  a  trace  will  appear  at  the  side  and,  when  the  current  is  reversed, 
a  similar  trace  on  the  opposite  side  and  at  nearly  the  same  distance  from 
the  center  one.  In  photograph  58,  Plate  I.,  two  values  of  the  current 
were  used  which,  with  the  central  magnetically  undeflected  exposure, 
make  five  traces  on  the  plate.  The  magnetic  deflection,  z,  was  taken  as 
half  the  distance  between  two  corresponding  points  of  corresponding 
traces.  The  electrostatic  plates  were  mounted  horizontally.  Each 
particle  then  describes  an  arc  of  a  parabola  in  the  vertical  plane  and  an 
arc  of  a  circle  in  the  horizontal  plane. 

THE  ELECTROSTATIC  DEFLECTION. 

Let  d  be  the  distance  from  the  upper  electrostatic  plate  to  the  upper 
surface  of  the  photographic  plate  and  let  t  be  the  thickness  of  the  photo- 
graphic plate,  Fig.  3.  If  K  is  the  dielectric  constant  of  the  photographic 


k & M 

Fig.  3. 

plate  and   V  the  potential  difference  in  volts  of  the  two  electrostatic 
plates  the  force  on  unit  charge  due  to  the  electric  field  is 

F        VXIO?  (* 

d  +  t/K' 

This  force  produces  a  downward  acceleration  of  the  electron  such  that 

Ee  =  ma,  (2) 


59 


LLOYD  T.  JONES. 


[SECOND 

[SERIES. 


where  e  is  the  charge,  m  the  mass  and  a  the  acceleration  of  the  electron. 
If  ti  is  the  time  required  for  the  electron  to  fall  to  the  photographic  plate 
we  shall  have 

vtl  =  v//2  +  z2,  (3) 

where  v  is  the  velocity  of  the  electron.  Equation  (3)  is  true,  since  z 
is  small  enough  in  comparison  with  /  that  the  chord  may  be  considered 
equal  in  length  to  the  arc.  Then 


and,  since 
we  get 


d  = 


d  =  =X2, 
Ee  P  +  z2 


(4) 
(5) 
(6) 


2m      v2 
Substituting  the  value  of  E  from  equation  (i)  and  rearranging  we  have 

mv2       V(l2  +  22)io8 


e     ~  2d(d  +  t/K)  ' 


(7) 


THE  MAGNETIC  DEFLECTION. 

If  the  plane  of  the  photographic  plate  be  considered  as  in  the  plane  of 
this  page  with  the  source  of  cathode  rays  at  the  origin,  0,  of  the  set  of 
axes  shown  in  Fig.  4,  the  arc  of  the  circle  shown  will 
be  the  projection  on  the  photographic  plate  of  the  elec- 
tron's path  and  will  show  accurately  the  curvature  of 
the  path  due  to  the  magnetic  field.  Let  z  be  the  mag- 
netic deflections,  measured  as  previously  mentioned, 
and  let  /  again  be  the  x  distance  to  where  some  electron 
of  velocity  v  strikes  the  plate.  If  r  is  the  radius  of  cur- 
vature of  the  circular  path  due  to  the  magnetic  field,  the 
length  of  the  projection  on  the  photographic  plate  of 
the  actual  path,  or  the  arc  shown,  will  be 

rB  =  vh,  (8) 

where  0  is  the  angle  at  the  center  of   the  circle  sub- 
tended by  the  arc. 

From  Fig.  4  we  see  that 


4. 


and  that 


But 


tan 


r  —  z 


(9) 


(10) 


VOL.  VIII.-J  VARIATION  OF  MASS  WITH  VELOCITY.  60 


No.  i. 


+  COS  6 

and  from  Fig.  4 


6  I   —  COS  6 

tan  -  =  Ji  (n) 

2         X   I 


cos  6  =  --  .  (12) 


Then 


and 

1  =  ^'  •    (I4) 

whence 

P  +  z* 
r=—-*  (15) 

The  magnetic  force  on  the  particle,  due  to  the  field  H,  is  perpendicular 
to  the  direction  of  motion  of  the  particle  and  hence  has  only  its  component, 
Hev  cos  0,  in  the  y  direction.  Since  only  this  component  produces  the 
deflection  z,  we  shall  find  the  average  force,  /,  on  the  particle  and  use 
this  value  for  the  magnetic  force. 


Hev  I    cos  Odd  .     . 

7  J  rr      Sin  &  t    ^ 

/=-        —       -=&.—  .  (16) 

This  force  gives  the  electron  an  acceleration  a\  in  the  y  direction.     Then 

sin  6 


(17) 

and 

z  =  \a^.  (18) 

From  equations  (8)  and  (18)  we  have 


and  from  (17) 

e        sin  6 

"-«*•—'  (20) 

On  substitution  of  the  values  from  (19)  and  (20)  in  equation  (18)  we 
get 

e  Hr20  sin  0 

z  =  --        --  .  (21) 

m        2v 

From  Fig.  4 

sin  0  =  ~  ,  (22) 

and,  with  an  approximation, 


6 1  LLOYD  T.  JONES.  [lS?ESD 


+  z2.  (23) 

Substituting  these  values  in  (21)  we  find 

z  =  — -N//2  +  s2  (24) 

mv   2 

or 

/_-\ 

^  =  tfv7?T^' 

From  equations  (7)  and  (25)  we  obtain  the  desired  expressions, 


X  io8 
Hld(d  +  t/K) 
and 

e          z2V2  X  io8 


m  ~  HH^d(d  +  t/K)  ' 

For  any  single  photograph  taken  with  constant  deflecting  fields  equation 
(27)  may  be  written  in  the  form 

z  =  C^e/m,  (28) 

where  C  is  a  constant. 

This  equation  shows  the  traces  to  be  straight  lines  for  constant  values 
of  e/m  and  that  the  outer  traces  should  curve  toward  the  central  one  for 
the  higher  velocities.  From  the  way  e/m  enters  the  equation  one  would 
expect  only  slight  curvature  of  the  traces  unless  e/m  diminished  very 
rapidly.  The  equation  shows  that  only  the  ratio  z/l  or  the  slope  of  the 
straight  lines  need  be  obtained  from  the  photographic  plates.  This 
method  is  thus  made  one  of  particular  value  for  the  determination  of 
e/mo,  for  slow  velocities,  as  it  permits  easy  averaging  of  values. 

THE  EARTH'S  FIELD. 

In  fastening  the  apparatus  to  the  stone  pier  it  was  carefully  placed 
so  that  the  undeflected  beam  travelled  horizontally  in  the  direction  of 
the  earth's  field.  The  effect  of  the  vertical  component  of  the  earth's 
field  was  then  to  increase  the  one  deflection  of  the  magnetic  field  and  to 
lessen  the  deflection  when  the  current  was  reversed.  From  an  inspection 
of  the  equation  it  is  seen  that  the  effect  of  this  vertical  component  may 
be  neglected  as  it  cancels  due  to  the  method  used  in  measuring  z. 

The  beam  of  electrons  travelled  from  north  to  south  so  that  when  only 
the  electrostatic  field  bends  it  downward  it  cuts  the  horizontal  component 
of  the  earth's  field  at  a  small  angle.  The  central  trace  is  thus  thrown  a 
little  to  one  side. 

Let  HI  be  the  value  of  the  horizontal  component  of  the  earth's  field. 


°L'VI11' 


N°oL'iVI11']  VARIATION  OF  MASS  WITH  VELOCITY.  62 

When  the  electron  is  deflected  magnetically  it  has  a  component  velocity 
at  right  angles  to  the  magnetic  field  HI  and  therefore  has  a  small  force 
acting  on  it.  This  force  will  aid  or  oppose  the  force  of  the  electrostatic 
field  depending  on  the  direction  of  the  magnetic  deflection.  This  small 
force  due  to  HI  was  found  to  be  negligible. 

It  follows  then  that  a  small  error  made  in  placing  the  apparatus  such 
that  the  beam  would  travel  neither  quite  horizontally  nor  exactly  in  the 
magnetic  meridian  would  have  no  appreciable  effect  on  the  results  of  the 
experiment. 

The  dielectric  constant,  K,  of  the  photographic  plate  was  taken  as  6. 
Since  the  plate  is  in  contact  with  the  lower  electrostatic  plate  and  the 
electrostatic  field  is  on  for  ten  to  thirty  minutes  before  the  exposures  are 
made  the  value  of  the  constant  chosen  must  not  be  that  obtained  by  a 
method  not  allowing  for  the  accumulation  of  a  charge  by  the  glass.  It 
should  be  pointed  out,  however,  that  if  the  value  of  e/mQ  is  measured 
from  the  same  photograph  the  value  of  K  will  in  no  wise  affect  the  value 
of  the  ratio  m/wio  if  only  K  remain  constant.  It  will  enter,  however,  in 
the  determination  of  the  velocity  of  the  electron  but  the  error  thus  intro- 
duced is  relatively  small. 

The  deflecting  magnetic  field  was  kept  at  values  sufficiently  small  that 
z2  could  be  neglected  compared  with  I2.  The  equation  for  the  velocity 
then  becomes 

zV  X  io8 

(29) 


If  the  value  of  e/m  is  calculated  from  the  smaller  deflections,  ZQ  and  /0, 
on  a  photograph  the  ratio  m/niQ  for  the  higher  velocities  is  given  by 


The  individual  values  of  e/m  as  calculated  from  the  photographs  are 
shown  in  Fig.  5,  in  which  (as  well  as  in  Figs.  6,  7  and  8)  the  full  line  curves 
marked  "  A  "  and  "  L  "  correspond  to  the  theoretical  values  of  Abraham 
and  Lorentz  respectively.  Of  the  points  lying  above  both  of  these  curves 
all  except  three  are  due  to  a  single  photograph. 

The  ratio  of  the  masses  was  also  calculated  by  means  of  the  preceding 
equation.  To  test  which  of  the  theoretical  curves  the  points  collectively 
best  fit  it  was  assumed  that  the  value  for  the  slowest  velocity  electrons 
showing  on  each  of  the  photographs  was  a  value  exactly  fitting  the 
Lorentz  curve  and  the  other  values  were  plotted  by  using  only  the  ratio 
of  the  masses  as  calculated  from  the  photographs.  These  values  are 
set  down  in  Fig.  6.  Similarly  Fig.  7  shows  the  results  assuming  the 


LLOYD  T.  JONES, 


fSECOND 
[SERIES. 


value  for  the  slowest  velocity  showing  on  each  of  the  photographs  to  lie 
exactly  on  the  Abraham  curve.  Now  by  a  comparison  of  Figs.  6  and  7 
it  is  seen  that  in  either  case  the  points  fit  the  Lorentz  curve  more  nearly 
than  the  Abraham  curve. 


.7  9  /.*  1.3  l.S  1.7  J.t 


Fig.  6. 

Table  I.  gives  the  data  and  results  taken  from  one  pair  of  traces  on 
one  of  the  photographs. 

TABLE  I. 


/Cm. 

20  Cm. 

zJtCm. 

elm  X  I0~7- 

v  X  10-10. 

Remarks. 

3.93 

.1443 

.01836 

1.708 

.6089 

4.43 

.1587 

.01791 

1.625 

.6696 

6.93 

.2503 

.01806 

1.653 

1.056 

Photograph  58, 

7.43 

.2667 

.01795 

1.632 

1.125 

1,926  volts, 

7.93 

.2817 

.01796 

1.599 

1.189 

d  =  .8137  cm., 

8.43 

.2957 

.01754 

1.558 

1.247 

<*+//#  =  .  8418  cm. 

8.93 

.3107 

.01740 

1.533 

1.311 

9.43 

.3250 

.01723 

1.504 

1.371 

9.93 

.3427 

.01726 

1.508 

1.446 

10.43 

.3583 

.01718 

1.495 

1.512 

PHYSICAL  REVIEW,  VOL.  VIII.,  SECOND  SERIES. 
July,  1916. 


PLATE  II. 
To  face  page  64. 


Photograph  63. 


Photograph  64. 


Photograph  66. 


Photograph  68. 

LLOYD    T.  JONES. 


PHYSICAL  REVIEW,  VOL.  VIII.,  SECOND  SERIES. 
July,  1916. 


PLATE  I. 
To  face  page  64. 


Photograph  54. 


Photograph  58. 


Photograph  59. 


Photograph  60. 

LLOYD    T.  JONES. 


VOL.  VIII.l 
No.  i. 


VARIATION  OF  MASS  WITH  VELOCITY. 


64 


Fig.  8  represents  graphically  the  results  shown  in  Table  I. 

On  each  of  the  photographs  the  lines  seen  crossing  the  electron  paths 
were  drawn  between  the  jaws  of  a  pair  of  vernier  calipers.  The  photo- 
graphic plate  while  in  position  touched  the  ebonite  disc,  L,  Fig.  I,  and 
hence  the  length  of  the  iron  slip,  P,  determined  the  distance  of  the  opening 


1.9 


Fig.  7. 


from  the  end  of  the  photographic  plate.  On  each  of  the  photographs  the 
line  near  the  right  is  that  marking  the  opening  and  the  others  show  the 
successive  values  of  /  for  which  the  values  of  elm  and  v  were  calculated. 


In  several  of  the  photographs,  54  for  instance,  the  lines  could  be  seen 
nicely  with  the  unaided  eye  but  were  too  dim  when  seen  through  the 
comparator  microscope.  These  lines  were  touched  with  a  sharp  pencil 
and  these  marks  used  to  determine  the  position  of  the  lines.  The 
photographs  show  very  easily  which  of  the  lines  were  so  treated. 

The  distance  apart  of  the  traces,  22,  was  measured  by  a  comparator 
reading  to  .005  mm.  The  value  of  22  for  each  distance  was  measured 


65  LLOYD  T.  JONES. 

five  times,  usually  on  different  days,  and  the  average  taken.  Usually 
no  measurement  differed  more  than  .001  cm.  from  the  average  and  almost 
never  did  one  differ  more  than  .002  cm.  The  comparator  screw  was 
calibrated. 

It  was  found  experimentally  that  the  distortion  of  the  magnetic  field 
due  to  the  iron  of  the  constricting  canal  had  the  effect  of  making  the  mag- 
netic deflection  smaller.  It  may  be  considered  as  zero  for  a  small  distance 
p  further  and  then  constant  for  the  remainder  of  the  path.  This  has  the 
effect  of  making  /  smaller  and  hence  e/m  and  v  larger.  The  length  / 
does  not  enter  directly  into  the  value  of  v  unless  the  two  values  of  /  for 
the  distance  of  travel  in  the  two  fields,  electrostatic  and  magnetic,  are 
different.  The  value  1.765  X  io7  was  assumed  as  the  correct  value  of 
e/mo  and  the  two  curves  in  Figs.  5,  6  and  7  accordingly  point  to  this  value 
for  slow  velocities.  The  magnitude  of  the  factor  p  was  calculated  and 
this  value,  p  =  .07  cm.,  was  used  to  correct  all  the  values  of  I  used. 
This  correction  was  assumed  to  be  the  same  for  the  electrostatic  field. 

CONCLUSIONS. 

1.  The  method  used  in  the  present  investigation  does  not  necessitate 
a  homogeneous  cathode  beam. 

2.  Each  photograph  gives  a  trace  of  all  velocities  present  and  makes 
possible  a  verification  of  the  law  from  a  single  photograph. 

3.  The  cathode  beam  never  leaves  the  region  between  the  electrostatic 
plates.     The  uncertain  field  distribution  at  the  ends  of  the  plates  is  thus 
avoided. 

4.  The  present  investigation  has  been  carried  out  with  rays  of  a 
velocity  B  little  greater  than  any  previously  employed. 

5.  The  results  favor  the  Lorentz-Einstein  rather  than  the  Abraham 
formula. 

In  conclusion  I  wish  to  express  my  appreciation  to  Dr.  C.  T.  Knipp 
for  the  enthusiasm  with  which  he  has  followed  the  progress  of  the  work. 
Also  I  wish  to  express  my  thanks  to  Prof.  A.  P.  Carman,  director  of  the 
laboratory,  for  the  facilities  he  so  kindly  placed  at  my  disposal. 

LABORATORY  OF  PHYSICS, 

UNIVERSITY  OF  ILLINOIS, 
March  i,  1916. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  VIII,  No.  i,  July,  1916.  J 


ON  THE  INITIAL  CONDITION  OF  THE  CORONA  DISCHARGE. 

BY  JAKOB  KUNZ. 

r  I  ^HE  glow  discharge  of  electricity  surrounding  the  transmission  wires 
under  the  influence  of  high  potential  differences  has  been  studied 
by  electrical  engineers  of  England  and  America  in  recent  years.  In  the 
majority  of  these  investigations  alternating  current  has  been  used,  and 
very  definite  empirical  results  have  been  obtained.  Comparatively  few 
researches  have  been  carried  out  on  the  direct  corona,  among  which  those 
of  Watson,  Schaffers  and  S.  P.  Farwell1  may  be  mentioned.  Farwell 
especially  has  shown  that  the  phenomena  are  far  more  complicated  than 
what  has  been  revealed  by  the  use  of  alternating  potentials. 

Before  making  an  attempt  at  an  explanation  of  some  of  the  phenomena 
I  wish  to  describe  briefly  the  various  forms  of  the  corona  due  to  direct 
current  potentials.  There  is  hardly  another  electric  phenomenon  which 
shows  the  difference  between  positive  and  negative  electricity  in  so  many 
different  ways  as  the  corona.  There  are  electric,  optical  and  mechanical 
differences.  For  very  small  wires  the  negative  glow  appears  before  the 
positive,  for  larger  sizes  the  positive  glow  appears  before  the  negative. 
The  boundary  between  the  two  regions  is  a  diameter  of  about  0.075  mm. 
The  positive  corona  in  air  forms  a  very  even  uniform  layer  of  light  of 
practically  constant  thickness.  The  negative  corona  on  the  other  hand 
starts  also  in  a  uniform  layer  of  red  light,  but  very  quickly  breaks  up  into 
bright  beads,  separated  from  each  other  by  dark  intervals.  Especially 
at  lower  pressures  this  difference  between  positive  and  negative  polarity 
is  very  conspicuous.  The  negative  beads  distribute  themselves  in  nearly 
equal  intervals  and  are  fairly  stable,  so  that  they  can  be  photographed 
readily.  The  positive  discharge  from  the  wire  in  a  coaxial  cylinder  has 
never  been  found  to  break  up  into  beads,  but  if  the  discharge  takes  place 
between  two  parallel  wires,  then  at  higher  potentials  the  positive  column 
of  light  also  breaks  up  into  shorter  intervals  and  finally  into  beads.  The 
question  arises  as  to  whether  the  beads  are  connected  with  irregularities 
on  the  surface  of  the  wire,  or  whether  it  is  an  intrinsic  phenomenon,  inde- 
pendent of  the  surface  irregularities.  The  number  of  beads  depends  on 

1  Watson,  Electrician,  London,  Vol.  63,  p.  828,  1909;  Vol.  64,  p.  707  and  776,  1909-10. 

Schaffers,  Comptes  rendus,  July,  1913,  p.  203. 

S.  P.  Farwell,  Transactions  of  American  Institute  of  Electrical  Engineers,  Nov.  13,  1914. 


2 9  JAKOB  KUNZ. 

the  pressure  of  the  gas  and  on  the  potential  difference.  If  these  two 
variables  are  kept  constant,  the  number  of  beads  remains  constant, 
indicating  that  the  beads  on  smooth  wire  are  an  intrinsic  phenomenon  of 
the  negative  discharge.  In  addition  special  experiments  have  been 
performed  with  polished  and  chemically  corroded  silver  wires  in  order  to 
test  this  conclusion.  For  a  given  potential  difference  the  corona  current 
increases  with  decreasing  diameter  of  the  wire,  and  with  decreasing  pres- 
sure. 

The  characteristic  curve,  like  the  starting  point  of  the  corona,  depends 
on  the  polarity  and  diameter  of  the  wire.  For  wire  smaller  than  0.077 
mm.  diameter  the  current  from  the  negative  wire  is  greater  than  that 
from  the  positive  wire.  For  the  diameter  of  0.077  mm-  the  currents  for 
opposite  polarity  coincide  accurately  over  a  certain  range  of  voltages 
above  the  critical  voltage,  and  then  the  negative  current  becomes  and 
remains  the  larger.  For  sizes  of  wire  larger  than  0.077  mm-  the  curves 
for  the  two  signs  cross  each  other.  For  the  lower  potential  differences 
the  positive  current  is  the  greater,  and  for  higher  potential  differences  the 
negative  current  is  the  greater.  Previous  investigators  already  found 
that  the  relation  between  the  electric  force  E  at  the  surface  of  the  wire 
and  the  radius  RI  is  given  by  the  formula 


where  EQ  and  b  are  constants,  E  is  calculated  by  the  electrostatic  formula: 

E-     -^ 


AF  being  the  potential  difference  between  the  central  wire  and  the 
cylinder  of  radius  R%.  For  the  smallest  sizes  of  wires  used,  the  relation 
between  E  and  RI  ceases  to  hold  as  can  be  seen  from  Table  I. 

The  critical  voltage  required  to  produce  visible  corona  depends  not 
only  on  the  radius  of  the  wire,  but  also  on  the  pressure.  At  very  low 
pressures  the  negative  corona  starts  before  the  positive  one,  at  higher 
pressures  the  positive  corona  starts  at  first.  The  characteristic  curves 
also  depend  on  the  pressure.  The  pressure  of  the  gas  and  the  radius 
of  the  wire  play  an  analogous  r61e,  very  thin  wires  seem  to  correspond  to 
low  pressures.  The  relation  between  the  pressure  p  of  air,  the  radius  RI 
of  the  central  wire  and  the  critical  electric  force  E  at  the  surface  of  the 
wire  is  given  as  follows: 


VOL.  VIII.l 
No.  i. 


INITIAL  CONDITION  OF  THE  CORONA  DISCHARGE. 


where  EQ  and  b  are  constants.  This  relation  holds  as  far  down  as  53 
mm.  Hg  pressure  for  the  positive  corona:  the  constants  £0  and  b  have 
different  values  for  the  positive  and  negative  wire. 

TABLE  I. 


y?  cm. 

jK+Volts. 

jE+Volts  per  cm. 

£+Calcul. 

y—  Volts/ 

E—  Volts  per  cm. 

E—  Calcul. 

0.00135 

2,720 

2.74X105 

2.62 

2,520 

2.52  X105 

2.55 

0.00218 

3,380 

2.58 

2.29 

3,230 

2.45 

2.23 

0.0023 

3,500 

2.25 

2.09 

3,300 

2.08 

2.04 

0.00258 

3,630 

2.12 

1.99 

3,500 

2.02 

1.94 

0.00386 

4,060 

1.66 

1.67 

4,060 

1.66 

1.65 

0.00678 

5,140 

1.31 

1.34 

5,320 

1.36 

1.33 

0.00825 

5,710 

1.25 

1.25 

6,140 

1.21 

1.21 

0.012 

6,600 

1.07 

1.09 

6,840 

1.09 

1.09 

0.013 

7,180 

1.07 

1.06 

7,660 

1.14 

1.06 

0.0205 

8,900 

0.93 

0.91 

9,370 

0.99 

0.92 

0.0325 

10,880 

0.80 

0.79 

11,440 

0.83 

0.80 

0.0385 

11,850 

0.77 

0.75 

12,400 

0.79 

0.76 

0.0512 

13,500 

0.71 

0.69 

14,120 

0.73 

0.71 

0.0642 

14,700 

0.65 

0.65 

15,220 

0.64 

0.64 

When  the  corona  starts,  the  pressure  of  the  gas  increases  suddenly. 
We  shall  call  this  pressure  ionization  pressure.  It  can  easily  be  measured 
by  means  of  a  sensitive  U-tube  open  manometer.  This  increase  of  the 
pressure  is  very  distinctly  different  from  the  increase  of  the  pressure  due 
to  the  evolution  of  Joule's  heat.  As  soon  as  the  current  is  interrupted  the 
ionization  pressure  sinks  suddenly  down  to  zero,  while  the  other  pressure 
increases  and  dies  out  gradually.  The  ionization  pressure  is  in  general 
for  a  given  potential  difference  larger  when  the  wire  is  negative  than  when 
it  is  positive,  but  the  difference  is  very  small,  if  not  opposite  at  the  be- 
ginning of  the  corona.  The  ionization  pressure  is  very  nearly  proportional 
to  the  current,  especially  when  the  wire  is  positive. 

The  ionization  pressure  as  well  as  the  fact  that  a  higher  potential 
difference  is  necessary  to  start  the  corona  for  thicker  wires  can  be  used 
with  advantage  for  the  construction  of  voltmeters,  some  of  which  are  in 
use  in  the  laboratory  of  the  University  of  Illinois. 

It  has  been  mentioned  that  the  negative  electricity  leaves  the  wire  in 
the  form  of  very  beautiful  beads  or  brushes,  mostly  evenly  spaced  along 
the  wire.  The  number  of  brushes  per  unit  length  depends  on  the  pres- 
sure and  on  the  potential  difference.  With  increasing  pressure  and  with 
increasing  potential  difference  the  number  of  beads  per  unit  length  in- 
creases and  their  brightness  at  the  same  time  decreases.  The  beads 
start  from  a  point  of  the  wire  and  spread  out  fanlike  in  a  plane  at  right 


31  JAKOB  KUNZ. 

angles  to  the  wire.  Very  interesting  is  the  influence  of  a  short  arc  in 
series  with  the  tube  upon  the  character  of  the  positive  and  negative  dis- 
charges. The  very  well  defined  positive  layer  of  light  spreads  out  con- 
siderably and  the  negative  brushes  disappear  almost  entirely,  giving  room 
to  a  continuous  glow,  whose  boundary  is  ill  defined;  in  other  words,  a 
very  short  spark  in  series  with  the  discharge  tube  destroys  the  difference 
in  the  appearance  between  the  positive  and  the  negative  corona.  This 
is  due  to  the  superposition  of  a  high  frequency  alternating  or  intermittent 
current.  A  small  change  of  the  spark  length  between  the  corona  and  the 
dynamos  produces  very  marked  differences  in  the  luminous  discharge. 
For  a  certain  spark  length  the  corona  assumed  the  form  of  bright  streamers 
which  fill  the  entire  space  between  the  wire  and  the  cylinder.  If  the 
spark  length  is  slightly  changed,  these  streamers  concentrate  into  a  few 
luminous  bands,  about  equally  spaced,  whirling  round  the  wire  and  pre- 
senting a  very  beautiful  aspect.  If  the  potential  difference  is  slightly 
increased,  this  phenomenon  is  replaced  by  the  arc,  which  is  apparently 
the  more  stable  form  of  discharge.  With  the  introduction  of  a  spark  a 
hissing  sound  will  be  heard  from  the  corona  tube. 

The  difference  between  positive  and  negative  elctricity  makes  itself 
felt  finally  in  mechanical  effects.  When  the  corona  takes  place  between 
two  parallel  wires  which  are  not  stretched  too  strongly,  the  negative 
wire  bows  in  toward  the  positive  and  the  positive  bows  away  from  the 
negative.  When  the  wires  are  purposely  made  rather  slack  the  positive 
wire  vibrates  strongly  with  a  circular  motion,  while  the  negative  wire 
remains  motionless. 

The  field  between  two  parallel  wires  and  between  a  cylinder  and  a 
coaxial  wire  has  been  explored  by  means  of  a  third  platinum  electrode. 
Even  before  the  corona  started  there  was  found  a  distortion  of  the 
electrostatic  field  especially  in  the  neighborhood  of  the  electrodes;  and 
in  many  if  not  in  all  cases  the  electric  force  at  the  surface  of  the  wires  is 
different  from  the  calculated  value  in  the  moment  when  the  corona  arises. 
The  observed  electric  force  seems  to  be  larger  than  that  calculated  from 
the  electrostatic  formula.  When  the  field  is  studied  in  the  space  between 
the  central  wire  and  the  coaxial  cylinder,  it  becomes  very  difficult  to 
explore  the  neighborhood  of  the  negative  wire,  where  the  potential  seems 
to  be  subject  to  continuous  changes.  The  exploration  of  the  field  around 
the  positive  wire  offers  no  difficulties. 

The  explanation  of  the  large  variety  of  phenomena  described  is  far 
from  being  complete.  An  attempt  at  an  explanation  of  some  of  the 
phenomena  will  be  made.  One  might  expect  that  luminous  discharge 
begins  when  the  electric  force  or  polarization  on  the  surface  of  the  wire 


VoL.JIII.j         INITIAL  CONDITION  OF  THE  CORONA  DISCHARGE.  32 

obtains  a  constant  value  required  for  the  ionization  of  the  molecules. 
It  has  been  found  however  that  the  critical  electric  force  is  given  by  the 
expression  : 


Various  values  for  E0  and  b  have  been  given,  for  instance,  E0  =  30, 
b  =  9  by  Y.  S.  Townsend.  Farwell  found  that  the  values  of  EQ  and  b 
are  distinctly  different  for  positive  and  negative  wires.  For  positive 
wires  he  found  E0  =  31.6;  b  =  8.43.  For  negative  wires  E0  =  35.0; 
b  =  8.06.  We  shall  now  assume  that  in  the  neighborhood  of  the  wire 
in  a  layer  of  constant  thickness  8.  a  certain  constant  energy  is  required 
for  the  beginning  corona,  different  for  positive  and  negative  electricity; 
indeed  the  splitting  up  of  the  molecules  into  ions  and  the  emission  of 
light  requires  energy.  When  a  sufficient  amount  of  energy  is  supplied, 
the  luminous  discharge  called  corona  will  occur.  It  has  been  shown  by 
Schaffers  that  the  thickness  8  =  0.07  cm.  of  the  luminous  layer  is  inde- 
pendent of  the  radius  of  the  wire.  In  the  neighborhood  of  the  wire,  the 
electric  force  E  assumes  large  values  so  that  the  polarization  also  is  large 
and  an  opposing  electric  force  £o  will  be  created,  so  that  the  resultant 
electric  force  is  equal  to  E  —  E0.  If  k  is  the  dielectric  constant,  RI  the 
radius  of  the  wire,  then  we  have: 

Ett  =  ~27rRl8(E  -  E0)2, 


If  Eg,  k  and  5  remain  constant,  then  we  have 

'"£  i 


the  rule  established  by  the  engineers.  E0,  Eg  and  8  are  obviously  different 
for  the  two  polarities  of  the  wire.  In  favor  of  this  theory  is  the  phe- 
nomenon of  beads.  When  a  thin  film  of  liquid  is  formed  along  a  thin 
thread,  the  film  on  account  of  the  surface  tension  breaks  up  into  beads; 
similarly  when  a  layer  of  electric  energy  is  formed  on  the  surface  of  the 
wire,  it  will  have  the  tendency  of  breaking  up  into  beads  extending  further 
away  from  the  wire  than  the  original  layer.  The  fact  that  the  negative 
discharge  is  much  more  apt  to  form  beads  than  the  positive  one,  seems 
to  be  connected  with  the  mechanism  of  the  discharge  itself.  When  the 
wire  is  very  thin  negative  electricity  escapes  easier  than  the  positive 
one,  just  as  in  the  case  of  very  sharp  points  and  at  very  low  pressures. 


33  JAKOB  KUNZ. 

The  negative  electricity  seems  to  escape  both  from  the  molecules  of  the 
gas  and  of  the  metal,  while  the  positive  electricity  consists  only  of  positive 
ions,  formed  in  the  air  alone,  as  no  positive  ions  escape  from  the  metal. 
The  positive  current  consists  of  positive  ions  alone,  the  negative  current 
of  negative  ions  and  electrons.  Now  it  seems  easier  for  the  electrons  to 
escape  in  a  few  places  from  the  metal  in  large  quantities,  than  from  the 
entire  surface  of  the  wire  in  smaller  quantities.  That  electrons  escape 
from  the  neighborhood  of  the  negative  wire  is  also  indicated  by  the  fact 
that  the  negative  wire  bows  in  toward  the  positive  one,  which  bows  away 
from  the  negative  one  and  that  under  the  same  circumstances  the  negative 
wire  remains  almost  motionless  while  the  same  wire,  when  charged 
positively,  carries  out  rotations  of  large  amplitude. 

For  very  small  wires  as  well  as  for  low  pressures  the  negative  corona 
starts  before  the  positive  one;  for  larger  wires  and  higher  pressures  the 
positive  corona  starts  before  the  negative.  The  negative  electricity 
seems  to  escape  in  the  form  of  electrons  easier  from  thin  metal  wires 
than  from  molecules  of  the  air.  This  phenomenon  suggests  that  the 
average  mass  of  the  ions  from  small  negative  wires  is  smaller  and  the 
mobility  larger  than  from  larger  negative  wires. 

Y.  S.  Townsend2  has  given  another  theory  of  the  initial  conditions  of 
the  glow  discharge  from  wires,  where  he  assumes  the  same  values  of  the 
constants  E0  and  b ;  and  applies  the  same  theory  to  the  corona  as  to  the 
spark  discharge.  The  two  phenomena  are  however  in  many  respects 
different. 

The  law  for  ionization  of  a  gas  by  collision  can  be  expressed  as  follows : 

-=/(-)• 

.  P    J\pr 

Y.  S.  Townsend  made  an  interesting  application  of  this  rule,  based  on 
experiments  at  low  pressures,  to  the  corona  and  spark  discharge,  which 
phenomena  he  considers  as  due  entirely  to  the  same  process  of  ionization. 
Let  us  choose  the  following  relations  between  the  two  cylinders  in  which 


Fig.  1. 
the  corona  occurs, 


1  Y.  S.  Townsend,  The  Electrician,  June  6,  1913,  p.  348. 


NoL'iVIIL]         INITIAL  CONDITION  OF  THE  CORONA  DISCHARGE.  34 


ds  =  zds', 

z  being  a  given  constant  number.     V  =  A  V  is  equal  to  the  potential  differ- 
ence applied  in  both  cases: 

p  V  p,  _  V  E, 

' 


7?  '  "~  7?    ~"    z    * 

&  log  £  *!'  log  ^       ««!  log  =i 

-Kl  Xti  AI 

E2  =  £1/2  holds  not  only  on  the  surface  of  the  inner  wire  but  in  any  two 
corresponding  points  such  as  A  and  A'  or  B  and  B'. 

The  number  of  ions  formed  by  collision  when  a  negative  ion  travels 
over  the  distance  AB  =  ds  is  given  by: 


=  pdsf(~). 


P 

The  number  of  ions  produced  in  the  second  experiment  over  the  distance 
ds'  is  given  by: 


z 
El 


/  ?  \ 
a'ds'  -AMf.l  j~)  =  ads> 


a  negative  ion  traveling  through  the  distance  ds  produces  the  same 
effect  as  over  the  distance  ds' .  The  same  holds  for  the  collision  of  positive 

ions. 

fids  =  fids', 

hence  we  have  the  same  effects  in  both  tubes.  A  given  potential  differ- 
ence V  causes  the  same  phenomena  in  both  tubes.  If  V  is  sufficient  to 
start  corona  in  one  cylinder,  it  will  also  give  rise  to  it  in  the  other  cylinder. 
If 

P 
Rzp'  =  zR%  ~  —  R-2,P\ 

if 

Ri'P'  =  RiP 
and  if 

V=  V 
then 

RI'EI  =  EiRi. 

Rip  is  therefore  only  a  function  of  RiEi.  If  we  keep  RiEi  constant, 
Rip  remains  constant. 


35 


JAKOB  KUNZ. 


[SECOND 

[SERIES. 


This  theory  applies  to  the  beginning  spark  as  well  as  to  the  beginning 
glow  discharge.  It  does  not  give  an  answer  to  one  of  the  first  questions 
regarding  the  corona  discharge,  namely,  is  the  current  due  to  ionization 
by  negative  or  positive,  or  to  both  ions? 

Now  the  following  relation  holds  between  the  critical  electric  force  EI 
and  the  radius  RI 


or 


—=L  , 

^  RI 

bRl  -  i 


for  p  = 


But  if  we  keep  RI  -  I  -  =  Rip  =  constant,  then  E^i  remains  constant. 

h~R,<h 

EiRi  =  E0Rip  H 


bp 


-Ei  = 


a  rule  that  has  been  established  by  the  engineers,  before  the  theory  was 
developed. 

TABLE  II. 


/in  Mm. 

+  ^ 
in  Volts. 

+£i  Volts 
per  Cm.  X  10*. 

+  -EI 

Calcul. 

y 

-El 

Calcul. 

2. 

720 

0.765 

0.33 

580 

0.615 

0.33 

10.9 

940 

0.998 

0.80 

870 

0.925 

0.81 

18.9 

1,110 

1.18 

1.07 

1,200 

1.275 

1.08 

53.2 

1,770 

1.88 

1.88 

1,920 

2.04 

1.94 

91.3 

2,350 

2.50 

2.56 

2,580 

2.74 

2.64 

173.5 

3,450 

3.60 

3.72 

3,750 

3.99 

3.86 

248.5 

4,250 

4.51 

4.65 

4,610 

4.90 

4.84 

334.8 

5,120 

5.42 

5.58 

5,520 

5.86 

5.86 

483.6 

6,660 

7.08 

7.11 

7,120 

7.55 

7.45 

616.6 

7,800 

8.29 

8.33 

8,330 

8.85 

8.77 

720.0 

8,730 

9.28 

9.21 

9,210 

9.80 

9.72 

746.0 

8,980 

9.51 

9.51 

9,530 

10.1 

10.1 

768.3 

9,100 

9.67 

9.65 

9,640 

10.2 

10.2 

Table  II.  gives  as  function  of  the  pressure  the  electric  force  at  the  sur- 
face of  the  wire  given  by  the  potential  difference  V  and  the  radii  and  cal- 


VOL^VIII.J  INITIAL  CONDITION  OF  THE  CORONA  DISCHARGE.  36 

culated  by  the  last  formula  for  the  positive  and  negative  wire.  For  the 
positive  wire  the  rule  holds  from  atmospheric  pressure  down  to  53  mm. 
or  lower,  while  for  the  negative  wire  the  deviations  are  noticeable  for  much 
higher  pressures.  For  the  positive  wire  the  constants  E0  =  31.6; 
b  =  8.43  and  for  the  negative  wire  EQ  =  35.0;  b  =  8.06  have  been  used, 
values  that  have  been  determined  in  a  previous  set  of  experiments. 

If  ionization  by  collision  were  due  to  negative  ions  alone,  the  constants 
EQ  and  b  would  be  the  same;  their  difference  indicates,  that  either  negative 
and  positive  ions  act  as  agents  of  ionization  by  collision  or  that  another 
source  of  ionization  is  involved  in  the  beginning  corona. 

It  has  been  mentioned  that  the  pressure  of  the  gas  suddenly  increases, 
when  the  corona  appears.  We  shall  apply  the  principle  of  conservation 
of  energy  to  this  phenomenon  as  follows:  Let  the  pressure  of  the  gas  in 
the  corona  tube  be  equal  to  pQ,  let  the  potential  difference  applied  be 
equal  to  A  V,  the  current  i  and  the  volume  v  ;  the  pressure  will  rise  from 
po  to  pi;  the  work  done  by  the  current  is  equal  to  AW  and  consists  in  the 
ionization  of  the  gas  plus  the  radiation  of  light  U,  and  a  reversible  part  W\ 

&Vi  =  U+Wi. 

It  is  evident  that  if  the  current  increases  the  current  must  decrease 
with  increasing  pressure,  otherwise  a  finite  amount  of  electric  work 
AF  •  i  could  perform  an  infinite  amount  of  mechanical  work. 

After  this  first  process  we  shall  increase  the  pressure  from  the  outside 
by  dpi  by  means  of  the  work 

dWz  =  vdpi, 

so  that  the  pressure  rises  from  pi  to  pi  +  dpi.  Now  we  shall  try  to  reach 
the  same  final  state  of  the  gas  starting  from  the  same  initial  conditions. 
Only  this  time  we  shall  apply  external  pressure  at  first,  supplying  the 
work: 

dWz  = 


while  the  pressure  rises  from  p0  to  p<,  +  dpo.  Now  the  same  potential 
difference  A  V  applied  will  produce  a  current  i1  ',  and  the  work  done  by  the 
current  will  be  equal  to: 

^'  =  u'  +  W, 


and  the  pressure  will  rise  to  pi  +  dpi.  If  the  initial  and  the  final  con- 
ditions are  the  same,  then  the  principle  of  conservation  of  energy  leads 
to  the  following  equation: 

AW  -dW2  =  AW  -  dW3, 
U+Wi-  vdpi  =  U'  +  TF4  -  vdpo. 
AF(i  -  i')  =  v(dpi  -  dpo). 


37 

But 

i'  =  i  —  di, 

AVdi  =  vd(pi  -  po) 

v 
i  =  A  F  ^a  ~  ^  +  *°f 

that  is,  the  current  will  decrease  with  increasing  pressure  pi,  and  hence 
the  ionization  pressure  pi  will  increase  proportionally  to  the  current. 
Experiments  will  soon  be  published  which  will  show  that  this  conclusion 
holds  in  a  wide  range  of  currents  and  ionization  pressures. 

SUMMARY. 

A  description  of  the  numerous  phenomena  has  been  given  which  are 
connected  with  direct  current  corona.  The  difference  between  positive 
and  negative  electricity  appears  in  electrical,  optical,  mechanical  and 
probably  chemical  effects.  A  new  attempt  at  an  explanation  of  some 
of  the  relations  disclosed  by  experiments  has  been  made.  Relations 
between  the  critical  electric  force  at  the  surface  of  the  wire,  the  pressure 
of  the  air,  and  the  radius  of  the  wire  have  been  obtained.  The  constants 
in  these  relations  are  different  for  the  positive  and  the  negative  wire. 
The  principle  of  conservation  of  energy  has  been  applied  to  the  ionization 
pressure  and  it  is  predicted  that  over  a  certain  range  the  current  should 
be  directly  proportional  to  the  pressure  increase. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
March,  1916. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  VIII,  No.  3,  September,  1916.] 


DETERMINATION   OF   THE   LAWS   RELATING    IONIZATION 

PRESSURE  TO   THE   CURRENT   IN   THE   CORONA   OF 

CONSTANT  POTENTIALS. 

BY  EARLE  H.  WARNER. 

INTRODUCTION. 

THE  "  corona  "  is  the  glow  which  surrounds  conductors  when  there 
exist  high  potential  differences  between  them  and  neighboring 
bodies.  A  careful  study  of  the  corona  phenomena  is  necessary  (i)  to 
determine  the  factors  which  regulate  the  loss  of  power  due  to  the  corona, 
which  on  long  transmission  lines  may  be  an  important  item,  and  (2)  to 
obtain  data  from  which  a  theory  can  be  developed  which  will,  with 
mathematical  rigor,  explain  the  corona  effects.  The  first  of  these  objects 
has  been  quite  successfully  carried  out  by  Peek,  Whitehead,  Ryan  and 
others.  The  only  advances  toward  a  theoretical  explanation  of  the  corona 
have  been  made  by  Bergen  Davis1  and  Townsend.2  In  these  two  theories 
the  authors  have  assumed  that  the  corona  is  an  ionization  phenomenon. 
That  is,  they  assume  that  the  high  potential  difference  causes  the  few 
ions  which  are  always  present  in  a  gas  to  move  with  a  velocity  sufficiently 
great  to  break  the  molecules  with  which  they  collide  into  two  parts,  one 
bearing  a  positive  charge  and  one  a  negative  charge.  All  these  charged 
particles  then  move,  because  of  the  influence  of  the  field,  toward  one  or 
the  other  of  the  terminals.  The  presence  of  these  ions  thus  explains  the 
conductivity  of  the  gas  and  the  acceleration  of  the  ions  explains  the 
light  effect.  If  the  corona  is  an  ionization  phenomenon  one  would 
expect,  if  the  corona  apparatus  was  inclosed,  at  the  instant  the  corona 
appeared,  i.  e.,  at  the  instant  the  molecules  were  broken  up  into  ions,  that 
the  pressure  in  the  apparatus  would  increase;  because  according  to 
kinetic  theory  the  greater  the  number  of  particles  in  a  given  volume  the 
greater  the  pressure.  This  pressure  increase  was  first  discovered  by 
Dr.  S.  P.  Farwell,3  working  in  this  laboratory.  The  above  mentioned 
theories  assume  ionization  but  do  not  account  for  such  a  pressure  increase. 
Under  certain  circumstances  this  pressure  increase  can  amount  to  as 

1  "Theory  of  the  Corona,"  Proc.  A.  I.  E.  E.,  January,  1911. 

2  "The  Discharge  of  Electricity  from  Cylinders  and  Points,"  Phil.  Mag.,  May,  1914. 
r"The  Corona  Produced  by  Continuous  Potentials,"  Proc.  A.  I.  E.  E.,  November,  1914. 


286 


EARLE  H.  WARNER. 


["SECOND 
LSERIES. 


much  as  three  cm.  of  mercury.  This  pressure  increase  can  not  be  due 
to  the  heating  effect  of  the  current,  because  it  occurs  very  quickly  and  if 
the  current  is  broken  in  a  few  seconds,  the  pressure  at  once  returns  to  its 
initial  value.  The  heating  effect  of  the  current  becomes  noticeable  only 
after  several  seconds  and  then  when  the  current  is  broken  the  pressure 
does  not  at  once  return  to  its  initial  value  but  it  requires  some  time  for 
the  heated  gas  to  cool  off.  Since  the  conception  of  ionization  is  so  in- 
timately associated  with  the  idea  of  increase  in  pressure,  it  seemed 
important  to  determine  the  laws  relating  this  ionization  pressure  to  the 
corona  current. 

THEORY. 

Dr.  J.  Kunz  has  developed  a  theory  which  predicts  how  this  pressure 
increase  should  vary  with  the  current.  One  can  best  understand  his 
development  by  thinking  of  the  corona  as  occurring  around  a  wire  which 
is  coaxial  with  a  cylinder.  See  Fig.  I,  which  represents  a  cross  section 

P 


•v 


Fig.  2. 

of  such  a  corona  tube.  Suppose  the  ends  of  the  tube  to  be  closed,  so 
as  to  inclose  a  constant  volume  VQ.  When  the  wire  is  connected  to  a 
very  high  positive  potential  and  the  case  grounded  the  corona  glow 
appears  around  the  wire  and  the  pressure  instantly  increases  from  at- 
mospheric to  some  higher  value.  Let  the  condition  of  the  gas  at  the 
beginning  of  the  experiment  be  represented  by  the  point  A ,  on  the  p  —  v 
plane.  (See  Fig.  2.)  The  volume  is  then  VQ  and  the  pressure  p0. 

Step  I. — Apply  a  potential  difference  e  between  the  wire  and  the  case. 
Some  current  i  will  flow  and  the  pressure  will  immediately  jump  from  pQ 
to  a  higher  value,  say  pi.  The  state  of  the  gas  will  now  be  represented 
by  the  point  C.  The  work  done  by  the  current  per  second,  ei,  will 
then  be  equal  to  the  increase  of  internal  energy  of  the  gas  AC/",  plus  the 
work  done  by  the  gas  Wi,  due  to  the  pressure  increase.  This  energy 
equation  gives  us 

-  TP,.  (i) 


Step  II. — Let  us  force  into  the  tube  a  small  amount  of  gas.     This 


VoL.^VIII.j  CONSTANT  POTENTIALS.  287 

will  require  work  dW2  and  the  pressure  will  increase  from  pi  to  pi  +  dpi 
and  can  be  represented  by  the  state  point  B.     Then 

dW2  =  -  vrfpi.  (2) 

The  total  work  to  change  the  gas  from  state  A  to  state  B  has  then  been 

ei  +  dW2  =  AU  +  Wi  -  vodpi.  (3) 

Now  let  us  start  again  with  the  same  initial  conditions  and  by  two 
different  steps  arrive  at  the  same  final  condition. 

Step  III. — When  the  state  of  the  gas  is  A  let  us  force  in  a  small  amount 
of  gas.  This  will  require  work  dW3  and  the  pressure  will  increase  from 
PQ  to  pQ  +  dpo,  which  may  be  represented  by  the  state  point  D.  Then 

dWs  =  —  v0dpQ.  (4) 

In  the  existing  conditions  the  size  of  the  current  depends  not  only  on 
the  potential  difference  but  also  upon  the  initial  and  final  pressures. 
The  increase  in  current  causes  an  increase  in  pressure  which  tends  to 
'stop  the  current.  The  steady  condition  of  the  current  represents  a 
condition  of  equilibrium  between  the  attempt  of  the  current  to  increase 
the  pressure  and  the  attempt  of  the  increased  pressure  to  stop  the  current. 

Step  IV.  Now  apply  the  same  potential  difference  e.  Let  that 
current  ir  flow  so  that  it  will  cause  the  pressure  to  increase  from  po+dpQ 
to  pi  +  dpi,  that  is,  so  that  the  state  of  the  gas  can  be  represented  by  B. 
Then  as  in  Step  I. 

ei'  =  AU'+Wt.  (5) 

In  the  last  two  steps  the  total  work  required  to  change  the  state  of 
the  gas  from  A  to  B  is 

ei'  +  dWz  =  AU'  +  W4  -  M/>o-  (6) 

Then  by  the  law  of  the  conservation  of  energy,  the  work  required  to 
change  a  system  from  one  state  to  another  is  independent  of  the  path, 
we  have 

&U  +  Wi  -  vodpi  =  AC/'  +  W*  -  vQdpQ  (7) 

or 

AC/  -  AC/'  +  Wi  -  W,  =  vQ(dpi  -  dp*).  (8) 

Subtracting  (5)  from  (i)  we  have 

At/  -  AC/'  +  Wi  -  W,  =  e(i  -  i').  (9) 

Therefore 

e(i  -  i')  =  vQ(dpi  -  dpo).  (10) 

But 

i  =  i'  +  di. 
Then 

edi  =  v<>d(pi  -  pQ)  (ii) 


288 


and  integrating 


EARLE  H.   WARNER. 


=  ~  (Pi  —  Po) 


a  constant. 


[SECOND 

[SERIES. 


(12) 


Since  (pi  —  pQ)  represents  the  increase  in  pressure,  that  is,  the  ioniza- 
tion  pressure,  this  equation  shows  that  the  ionization  pressure  should  be 
exactly  proportional  to  the  corona  current. 

It  was  the  object  of  the  experiments  which  have  been  performed  to 
test  this  relationship  with  pure  gases  in  the  tube. 

APPARATUS. 

The  constant  potentials  were  obtained  from  a  battery  of  continuous 
current  shunt-wound  5OO-volt  generators  connected  in  series. 

The  corona  tube  was  of  the  wire  and  coaxial  cylinder  type.     (See  Fig. 


Fig.  3. 

3.)  Glass  plates  with  holes  for  the  wire  to  pass  through  were  sealed  to 
the  ends  of  the  tube  so  that  the  holes  were  on  the  axis  of  the  cylinder. 
The  wire,  No.  32,  copper,  passed  through  the  holes  and  was  thus  coin- 
cident with  the  axis  of  the  cylinder.  The  wire  was  sealed  into  these 
holes  and  held  taut  by  red  sealing  wax.  To  the  cylinder  was  soldered  a 
small  "  T  "  tube,  one  side  of  which  was  joined  to  the  vacuum  pump  and 
the  other  side  was  connected  to  a  Bristol  aneroid  pressure  gauge. 

The  increase  in  pressure  was  measured  by  this  Bristol  gauge.  Any 
increase  in  pressure  caused  it  to  bend  slightly  and  so  rotate  the  mirror. 
By  observing  the  deflection  of  a  beam  of  light  over  a  scale,  which  had 


VOL.  VIII. 
No.  3. 


CONSTANT  POTENTIALS. 


289 


previously  been  calibrated  by  reading  simultaneously  the  deflected  beam 
and  a  water  manometer  connected  directly  to  the  gauge,  the  increase  in 
pressure  in  cm.  of  water  could  be  determined.  The  advantage  of  such  a 
pressure  measuring  instrument  in  this  experiment  is  that  it  is  very  quick 
in  its  action.  The  instant  the  pressure  increases  the  gauge  jumps  right 
up  to  its  new  position  and  a  reading  can  be  taken  in  a  very  few  seconds. 
It  was  necessary  to  read  this  pressure  increase  quickly  because  if  much 
time  was  required,  the  heating  effect  of  the  current  would  increase  the 
pressure  also. 

The  current  was  measured  by  a  Type  H  D' Arson val  galvanometer. 
The  apparatus  was  connected  as  is  shown  in  Fig.  4. 


Machine  Terminal*. 


Fig.  4. 


DISCUSSION. 

Experiments  were  made  when  the  wire  was  positive  and  the  case 
grounded  with  dry  air,  hydrogen,  nitrogen,  carbon  dioxide,  oxygen  and 
ammonia  as  the  gases  in  the  tube.  Considerable  care  was  taken  to  see 
that  these  gases  were  absolutely  pure.  They  were  all  dried  carefully 
before  they  were  used.  The  following  curves  (Figs.  5,  6,  7,  8,  9)  show 
graphically  the  results.  Fig.  10  shows  all  the  curves  plotted  to  the  same 
scale.  With  this  scale  the  hydrogen  curve  should  be  continued  until  its 
ordinate  is  equal  to  that  of  the  carbon  dioxide  curve. 

The  fact  that  the  points  all  lie  so  accurately  on  a  straight  line  shows 
conclusively  that  experiment  verifies  the  prediction  made  by  Dr.  Kunz's 
theory.  The  law  can  then  be  stated  that,  in  the  gases  studied  with  the 


290 


4; 

EARLE  H.  WARNER.                                                 [iSiEs 

Relation  Between 

• 

J 

, 

IOHIZATIOH  PHBSSURB  and  CORQHA  CURRBHT. 

/ 

I     3 

8 

c 

Hydrogen.     Wire  +. 

X 

/ 

x 

^ 

Increase  of  Pressure  1 
—  N 

> 

r" 

x 

£ 

/ 

X 

I            2.            3            A            5             6           7 

i 

10            fl             1 

I 

Current    la  10"*  Amperes. 


Fig.  5. 

wire  positive  the  ionization  pressure  is  exactly  proportional  to  the  corona 
current. 

In  the  case  of  oxygen  a  considerable  amount  of  ozone  was  formed  due 
to  the  corona  discharge.  Evidently  the  curve  as  shown  is  a  resultant 
of  two  effects:  (i)  A  chemical  change  due  to  the  formation  of  ozone. 
This  would  tend  to  cause  a  decrease  in  pressure.  (2)  The  increase  in 


a 

Relation  Between 

> 

8. 

IOXIZATIOK  PRB3SURB   and  COROTA  CURRBBT. 

ts 

Hitrogen«     Wire  +.• 

X 

/ 

X 

r 

/x 

*  r 

> 

' 

«° 

X 

0* 

^x^ 

5 

f! 

X 

' 

3 

S    3 

_x 

jS^ 

x 

! 

X 

i  ,. 

p/ 

x 

/ 

I  a        2.0.        3Q       40       -5Q        60       70.       SO.       30.       1 00       110.       IZO.      130 
Current  In  1Q-*  Amperee. 


Fig.  6. 


VOL.  VIII.l 
No.  3. 


CONSTANT  POTENTIALS. 


29I 


Relation  Between 

IOTIZATIOH  PRBSSURB  and  CORONA  CURRXHT. 
Carbon  Dioxide.  Wire  +. 


IZ.      13      14.      lo 


4-       5        67       O      9       10      I  (      \, 
Current   in  10'°  Amperes. 

Fig.  7. 

pressure  due  to  the  ionization  of  the  oxygen.  Since  the  ionization  curve 
is  a  straight  line,  as  is  shown  by  the  gases  in  which  probably  there  is  no 
chemical  action,  and  since  this  resultant  curve  of  oxygen  is  a  straight 
line,  the  following  law  can  be  stated : 

Whenever  chemical  change  takes  place  due  to  the  corona  the  chemical 
change  is  exactly  proportional  to  the  current. 


Relation  Between 

\ 

IOHIZATIOH  PRBSSURB  and  CORONA  CURKSHT. 

jT^ 

s3 

i 

h 

Oxygen.  Tire  +. 

/ 

S 

of  Preaaur*  in  Cm  o 
N 

/ 

/ 

, 

/ 

I  ' 

/ 

/ 

5 

Current  in  LO*8  'Ampere*. 

L.        2.5 

Fig.  8. 


292 


EARLE  H.  WARNER. 


[SECOND 

[SERIES. 


B 

*  2. 

3 
5  L5 

g 

M 

Relation  Between 
IONIZAT10N  PRESSURE  and  CORONA  CURRBHT. 
Ammonia.   Wire  •*•. 

. 

/ 

^ 

^ 

X 

2r 

X 

X 

25     J 

T5     1.     1.2.5    1.5    l.*75    2.0 
Current  in  10"8  Amperee. 

Fig.  9. 

With  the  wire  negative  beads  always  appear  on  the  wire,  and  since  the 
pressure  increase  varies  with  the  arrangement  of  the  beads  which  are 
not  stable,  it  is  impossible  to  accurately  verify  the  above  relationship. 
When,  instead  of  the  quick  acting  gauge,  an  ordinary  open  manometer 
which  is  slow  in  its  action  was  used,  it  was  discovered  that  the  same 
relationship  as  above  stated  is  very  nearly  true  for  the  wire  negative  as 
well  as  positive. 

The  increase  in  pressure  in  the  case  of  nitrogen,  showing  ionization, 
is  one  of  the  exceptional  cases  where  nitrogen  is  largely  ionized  at  low 
temperatures  and  thus  probably  chemically  active. 

How  nitrogen,  carbon  dioxide  and  ammonia  are  ionized,  are  questions 
which  require  further  study. 

The  arrangement  of  the  apparatus  could  be  used  as  a  high  potential 
voltmeter  by  simply  calibrating  the  increase  in  pressure  against  volts,  as 
determined  by  a  disc  electrometer. 


:  3 

i 

i, 
i . 


Relation  Between 

I05IZA7IOH  PRESSURE  and  CORONA  CURRENT. 
Wire  +. 


Fig.  10. 


Na"3VI11']  CONSTANT  POTENTIALS.  293 

SUMMARY. 

The  ionization  pressure  in  the  positive  corona  is  exactly  proportional 
to  the  corona  current  in  dry  air,  hydrogen,  nitrogen,  carbon  dioxide, 
oxygen  and  ammonia. 

Any  chemical  action  that  takes  place  due  to  the  corona  is  exactly  pro- 
portional to  the  corona  current. 

The  writer  wishes  to  acknowledge  his  indebtedness  to  Professor  A.  P. 
Carman  and  to  Dr.  Jakob  Kunz,  associate  professor  of  physics,  for  their 
deep  interest  and  helpful  suggestions  concerning  the  conduct  of  this  work. 

LABORATORY  OF  PHYSICS, 

UNIVERSITY  OF  ILLINOIS, 
May,  1916. 


DIRECT  CURRENT  CORONA  FROM  DIFFERENT  SURFACES 

AND  METALS. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S..  Vol.  VIII,  No.  4.  October, 


DIRECT  CURRENT  CORONA  FROM  DIFFERENT  SURFACES 

AND   METALS. 

BY  SYLVAN  J.  CROCKER. 

I.     INTRODUCTION. 

IT  has  been  shown  by  F.  W.  Peek1  and  by  S.  P.  Farwell2  that  the  corona 
discharge  is  quite  different  when  the  wire  is  positive  and  when  it  is 
negative.  The  starting  point  of  the  corona  as  well  as  the  characteristic 
curves  depend  on  the  polarity  of  the  wire.  When  the  wire  is  negative 
the  corona  assumes  the  form  of  bright  "  beads  "  which  are  strung  along 
the  wire  more  or  less  evenly,  the  number  of  the  beads  per  unit  length 
depending  on  the  pressure  of  the  gas  and  the  potential  difference  between 
the  wire  and  the  cylinder.  This  beautiful  but  complicated  phenomenon 
suggested  that  probably  the  surface  conditions  and  the  chemical  nature 
of  the  wire  might  influence  at  least  the  negative  corona  in  the  form  of 
beads. 

It  became  the  purpose  of  these  experiments  then  to  find  out  the  in- 
fluence of  the  surface  condition  of  the  wire  upon  the  starting  point  and 
the  characteristics  of  the  corona  discharge  phenomena. 

The  apparatus  used  consisted  of  a  metal  cylinder  (inside  diameter  3.63 
cm.),  with  a  longitudinal  slot  for  observation  (1.53  cm.  wide),  sealed  in  a 
glass  cylinder  and  arranged  in  such  a  manner  that  wires  of  different 
sizes  could  be  easily  strung  along  the  cylinder  axis.  It  was  possible  to 
readily  connect  the  tube  to  a  vacuum  pump  for  varying  the  pressure. 
The  high  potential  direct  current  was  taken  from  forty  500- volt  D.C. 
generators  connected  in  series.  The  machines  were  self-exciting  and 
could  be  cut  in  or  out  by  closing  or  opening  the  field  switches.  Smaller 
variations  than  500  volts  could  be  obtained  by  varying  the  speed  of  the 
driving  motors  or  by  the  adjustment  of  a  rheostat  which  was  connected 
in  the  field  of  one  of  the  machines. 

The  voltage  was  read  on  a  Kelvin  electrostatic  voltmeter  which  had 
been  calibrated  with  an  attracted-disc  electrometer.  The  current  was 
measured  with  a  D' Arson val  galvanometer  whose  figure  of  merit  was 
found  to  be  6.25  X  io~6  amperes. 

1  F.  W.  Peek,  Jr.,  Dielectric  Phenomena  in  High  Voltage  Engineering,  p.  27. 

2  S.  P.  Farwell,  "The  Corona  Produced  by  Continuous  Potentials,"  A.  I.  E.  E.,  November 
13. 


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DIRECT  CURRENT  CORONA.  345 


No.  4. 


Preliminary  Experiments. — Preliminary  experiments  were  made  using 
a  steel  wire  the  surface  of  which  was  polished  over  one  half  its  length 
and  corroded  with  nitric  acid  over  the  other  half.  When  the  wire  was 
placed  in  the  tube  and  corona  made  to  form  on  it  at  low  pressures,  the 
effect  of  the  surface  condition  was  made  evident  at  once.  Nos.  I  and  3 
in  Fig.  I  show  this  experiment.  The  right  half  of  the  wire  is  polished 
and  has  the  characteristic  negative  beads,  while  the  left  half  is  chemically 
corroded  and  only  a  soft  glow  appears  there.  This  glow  is  different 
from  the  characteristic  positive  glow  in  that  it  is  much  greater  in  diameter 
and  has  a  fuzzy  appearance  like  eider  down. 

Of  course  it  must  be  noted  here  that  this  condition  is  for  a  slightly 
higher  potential  than  that  at  which  the  glow  first  appears  and  that  the 
fuzzy  glow  eventually  breaks  into  the  beads  upon  raising  the  potential. 
However  the  beads  on  the  corroded  end  do  not  have  the  sharp  clear-cut 
appearance  as  those  on  the  polished  end,  but  are  fuzzy  and  less  well 
defined.  The  positive  glow  is  also  shown  in  Fig.  I,  No.  2,  under  these 
same  conditions,  but  it  presents  the  same  appearance  for  both  parts  of 
the  wire. 

The  first  experiment  led  to  the  trial  of  a  wire  whose  surface  was  not 
only  (i)  polished  and  (2)  corroded,  but  also  (3)  mechanically  abrased. 
The  differences  existing  here  were  also  very  striking  and  clearly  shown 
at  once.  Fig.  2  contains  photographs  of  the  negative  wire,  the  left  end 
being  abrased,  the  center  polished,  and  the  right  end  chemically  corroded. 

No.  4  shows  the  starting  of  the  corona  at  low  pressures  and  corre- 
spondingly low  voltages.  It  will  be  seen  that  the  beads  start  first  on 
the  polished  surface  (i),  while  the  corroded  surface  (2)  shows  no  glow 
and  the  abrased  surface  (3)  has  but  a  slight  brush  discharge  on  it.  The 
beads  on  (i)  are  very  large,  clear,  steady  and  quite  evenly  spaced. 

No.  5  shows  the  effect  of  a  slight  increase  in  voltage  where  the  glow 
now  appears  on  surface  (2)  and  the  beads  begin  to  form  on  surface  (3). 
Gradually  increasing  the  voltage  and  the  pressure  as  well  causes  the 
glow  to  become  brighter  on  (2),  the  beads  to  increase  on  (i)  and  (3). 
The  beads  on  the  abrased  portion  have  a  lateral  movement,  while  those 
on  the  polished  part  are  still  very  steady  and  clear. 

With  still  greater  increase  in  pressure  and  voltage  it  is  possible  to 
reach  a  condition  where  the  whole  length  of  the  wire  is  covered  with  clear, 
steady  and  evenly  spaced  beads  (see  No.  6).  Here  it  seems  that  the 
surfaces  all  act  very  nearly  the  same  regarding  the  formation  and  building 
up  of  the  corona  discharge. 

Now  when  the  pressure  is  increased  to  370  mm.  and  the  voltage  is 
increased  to  produce  the  discharge  it  is  found  that  the  corona  starts  first 


346  SYLVAN  J.  CROOKER.  [ 


SECOND 
SERIES. 


on  the  abrased  portion  and  that  it  is  only  on  this  part  clear  steady  beads 
can  be  obtained  (see  No.  8).  The  beads  on  the  corroded  part  are  fairly 
well  defined  but  they  are  in  an  agitated  state,  moving  back  and  forth 
on  the  wire.  Under  these  conditions  it  is  found  impossible  to  get  steady 
beads  on  the  polished  part  of  the  wire;  instead  of  the  clear  beads  there 
is  a  rather  knobby  glow  on  the  wire,  the  condensations  in  which  seem 
to  be  beads  trying  to  form. 

This  reversal  of  the  phenomena,  as  shown  in  Fig.  2,  where  the  clear 
beads  form  on  the  polished  surface  at  low  pressures  and  on  the  abrased 
surface  at  high  pressures,  has  been  found  to  be  a  real  one  for  steel  wire. 
The  corona  starts  first  on  the  polished  wire  for  low  pressures  and  begins 
on  the  abrased  or  corroded  wire  at  much  lower  potentials  for  high  pres- 
sures. 

An  enameled  german  silver  wire  was  fitted  in  the  tube  after  one  half 
of  its  length  had  been  freed  from  the  enamel  and  polished.  At  low 
pressures  for  the  positive  wire  the  characteristic  glow  would  appear  on 
the  polished  end.  The  enameled  end  would  have  several  small  star- 
like  spots  of  light  irregularly  distributed  over  it  appearing  at  points 
where  the  insulation  had  broken  down.  Keeping  the  wire  positive  and 
increasing  the  voltage  caused  very  bright  "  streamers  "  of  purple  light  to 
shoot  out  from  a  few  of  these  small  stars.  At  higher  pressure  and  higher 

Tube 

Purple  Streamers v 

Brig/it  Spot  on  Wire 


Section  Elevation 

Fig.  4. 

voltage  these  streamers  increased  greatly  in  number,  the  glow  spreading 
out  into  a  thin  fan-shape.  This  fan  would  slowly  oscillate  or  rock  back 
and  forth  about  the  bright  spot  on  the  wire  as  a  center.  Between  these 
fans  a  hazy  fog-like  glow  was  everywhere  present.  Upon  placing  an  arc 
in  series  with  the  wire  and  the  tube  this  fog  would  disappear  and  the 
fans  would  become  more  sharply  defined  and  more  steady. 

For  the  wire  negative  (see  Fig.  3,  No.  14)  it  was  impossible  under  any 
conditions  to  get  the  characteristic  negative  beads.  Neither  could  a 
glow  be  produced  on  the  polished  end,  the  only  discharge  present  was  on 
the  enameled  end  similar  in  appearance  to  the  small  stars  for  the  positive 
wire.  However  for  the  negative  wire  the  stars  were  intensely  bright 
and  in  slight  movement.  Fig.  3  shows  the  appearance  of  the  discharge 
from  the  enameled  wire  when  both  positive  and  negative.  Fig.  4  gives 


DIRECT  CURRENT  CORONA.  347 

details  of  the  structure  of  the  positive  purple  fans.  For  the  enameled 
wire  negative  the  starting  potential  was  much  lower  than  for  the  opposite 
polarity. 

Figs.  I  and  3  suggest  that  the  starting  point  of  the  corona  and  the 
characteristic  curves  depend  on  the  surface  conditions.  In  order  to  test 
this  suggestion  the  following  experiments  have  been  performed. 

II.    VISUAL  CORONA  AND  STARTING  POTENTIALS. 

Many  characteristic  curves  were  obtained  for  different  sizes  of  copper 
wire  where  the  surfaces  were  polished  and  abrased  and  many  more  char- 
acteristic curves  were  taken,  using  wires  of  copper,  steel,  aluminum,  and 
silver  where  the  surfaces  were  polished,  abrased  or  roughened,  and 
chemically  corroded  or  oxidized.  The  more  striking  results  will  be  given 
in  the  following  paragraphs. 

Preparation  of  Surfaces. — For  the  polished  surfaces  care  was  taken  in 
choosing  wires  without  kinks  or  surface  scratches.  These  wires  were 
polished  with  fine  emery  cloth  and  finished  with  chamois  and  jeweler's 
rouge  just  before  placing  in  the  tube. 

The  abrased  surfaces  were  prepared  by  rolling  the  wire  in  emery 
powder  between  two  hard  plane  surfaces.  Care  was  taken  to  have  the 
surface  abrased  uniformly  over  the  whole  length. 

The  corroded  surfaces  were  prepared  by  different  methods.  The 
surface  of  the  steel  wire  was  corroded  by  dipping  in  a  solution  of  nitric 
acid,  a  black  surface  resulting.  The  aluminum  wire  was  corroded  by 
allowing  it  to  remain  in  a  solution  of  sulphuric  acid  for  a  few  days.  The 
result  was  a  thin  white  coating.  For  copper  it  was  necessary  to  oxidize 
the  surface  by  passing  a  heating  current  through  the  wire  in  the  presence 
of  oxygen.  Since  large  quantities  of  ozone  are  produced  by  the  corona 
discharge  the  silver  wire  was  coated  with  a  layer  of  silver  peroxide  by 
allowing  the  corona  to  play  on  the  wire  for  some  time. 

The  phenomena  are  very  complicated.  Their  description  will  be 
carried  out  according  to  the  surface  condition  of  the  wire,  and  for  each 
individual  condition  three  pressures  will  be  considered. 

Wires  Polished. — The  general  appearance  of  the  corona  is  the  same 
for  all  polished  positive  wires,  and  differs  but  slightly  for  negative  wires 
at  the  different  pressures.  At  pressures  of  about  50  mm.  when  the  po- 
tential is  brought  up  to  the  glow  potential,  wire  positive,  a  very  faint 
flashing  glow  is  seen  over  the  whole  length  of  the  wire,  which  becomes  uni- 
form and  steady  as  the  potential  is  raised  slightly.  The  potential  may 
be  carried  up  to  the  arcing  point  without  changing  the  general  appearance 
of  the  uniform  glow.  The  only  noticeable  change  is  an  increase  in  the 
brightness  of  the  bluish  glow. 


SYLVAN  J.  CROOKER. 


("SECOND 

[SERIES. 


For  pressures  of  50  mm.  and  negative  wire,  the  first  appearance  of  the 
corona  is  a  flashing  glow,  similar  to  that  for  positive  wire,  but  of  much 
greater  diameter  and  brighter.  Increasing  the  potential  causes  this 
glow  to  remain  steady  on  the  wire,  becoming  uniform  and  very  bright. 
Very  little  current  flows  until  a  stage  is  reached  not  far  above  the  starting 
point,  where  the  bright  uniform  glow  breaks  into  large  clear  character- 
istic negative  beads.  From  this  point  on  the  current  increases  rapidly 
with  the  potential.  As  the  potential  is  increased  the  beads  increase  in 
number  but  remain  large  and  well  defined,  this  will  be  discussed  more 
fully  later  on. 

For  the  polished  surfaces  and  pressure  of  50  mm.  the  negative  corona 
on  copper  begins  at  a  lower  potential  than  the  positive.  Corona  appears 
at  the  same  potential  for  both  polarities  in  the  case  of  steel,  but  for  alu- 
minum and  silver  the  positive  glow  begins  at  the  lower  potential.  This 

TABLE  I. 

COMPARISON  OF  STARTING  VOLTAGES  FOR  DIFFERENT  SURFACES  AND  WIRES. 

All  wires  about  0.41  mm.  diameter. 

Copper. 


Polished 

Abrased 

Corroded 

Press. 

mm. 

Wire 
~     Volts.    H 

Press, 
mm. 

Wire 
~~    Volts. 

Press, 
mm. 

Wire 
Volts. 

50 
252 
731 

1,700 
2,650 
6,010 

1,780 
2,600 
5,760 

53.2 
253 
743 

1,680 
2,550 
5,600 

1,820 
2,800 
6,200 

50.3 
250 

1,650 
2,010 

1,660 
2,500 

Steel 


51.6 

1,710 

1,710 

52.2 

1,690 

1,740 

52.3 

1,750 

1,700 

252.4 

2,600 

2,600 

253.2 

2,770 

2,770 

252 

2,550 

2,710 

727.6 

5,660 

5,960 

736 

4,560 

5,830 

739.4 

4,810 

5,760 

Aluminum. 


50 

1,760 

1,720 

52 

1,660 

1,800 

51.9 

1,240 

1,690 

251 

2,820 

2,900 

251.5 

2,490 

2,900 

252 

2370 

2,66u 

74L1 

5,880 

6,180 

741 

5,010 

5,800 

745.3 

4,680 

5,880 

Silver. 


53.2 

1,850 

1,820 

52.3 

1,730 

1,740 

52.5 

1,850 

1,780 

252.1 

3,150 

3,050 

252.2 

2,600 

2,900 

252.2 

3,150 

3,000 

744.8 

4,210 

6,130 

743.2 

5,060 

5,850 

746 

5,760 

6,320 

is  shown  by  Table  I.,  which  contains  the  starting  potentials  for  the  dif- 
ferent metals  and  different  surface  conditions.  Table  I.  shows  no 
general  law.  With  the  exception  of  the  silver  wire  at  a  pressure  of  746 


DIRECT  CURRENT  CORONA. 


349 


mm.  the  starting  potential  for  the  corroded  wire  is  smaller  for  both 
polarities  than  for  the  polished  wire.  For  the  negative  abrased  wire  the 
starting  point  is  in  general  lower  than  for  the  polished  wire  with  only  two 
small  exceptions.  With  the  exception  of  silver  the  starting  point  of  the 
abrased  positive  wire  is  higher  than  that  of  the  polished  wire.  With 
increasing  pressure  the  differences  involved  by  abrasion  and  corrosion 
diminish.  The  largest  influence  is  found  for  aluminum  wire,  negative 
corroded  at  51  mm. 

For  pressures  of  about  250  mm.  the  glow  for  wires  positive  is  the  same 
as  before,  being  uniform  and  increasing  in  brightness  as  the  potential 
increases.  For  wires  negative  and  polished  it  was  almost  impossible 
to  break  the  glow  up  into  clear-cut  beads  at  this  pressure.  With  in- 
creasing potential  the  glow  would  become  brighter  and  would  condense 
at  certain  ill-defined  points  apparently  attempting  to  form  beads,  but 
these  condensed  regions  would  be  in  rapid  motion  back  and  forth  along 
the  wire. 

For  atmospheric  pressure,  wires  polished  and  positive,  the  glow  would 
appear  faint  but  uniform  and  would  increase  in  brightness  as  the  potential 
was  increased.  For  negative  wires  a  faint  flashing  glow  would  appear  at 
break-down  potentials  increasing  in  brightness  with  the  potential  increase. 
A  very  few  scattered  beads  would  at  times  be  formed,  but  they  would  be 
small  and  unstable  having  very  rapid  lateral  motion.  This  motion  would 
increase  in  amplitude  and  speed  with  increasing  voltage.  Clear  cut 
beads  over  the  whole  wire  was  impossible  here  as  in  the  last  case. 

Wires  Mechanically  Abrased.  —  With  wire  surfaces  mechanically  abrased 
or  roughened  and  pressure  of  50  mm.  the  positive  glow  begins  with  faint 
flashes  as  in  the  case  of  the  polished  surfaces,  the  glow  becoming  steady, 
uniform  and  increasing  in  brightness  as  the  potential  is  increased.  The 
starting  glow  voltage  is  in  general  higher  than  for  the  positive  polished 
wires,  and  is  also  higher  than  for  the  abrased  negative  wires.  For  wires 
abrased  and  negative  the  corona  begins  with  bright  flashes  of  a  fuzzy 
glow,  part  of  which  might  have  one  or  two  large  flashing  beads.  This 
flashing  glow  seemed  to  pulsate  in  synchronism  with  the  impulses  of  the 
driving  machinery.  A  slight  potential  increase  above  the  first  noticeable 
glow  would  cause  the  glow  to  break  into  well-defined  beads  which  would 
soon  become  steady  and  clear,  increasing  in  number  with  a  potential 
increase.  The  negative  starting  voltage  for  abrased  wires  is  lower  than 
for  the  polished  surfaces. 

For  wires  abrased  and  pressures  of  250  mm.  the  positive  visual  glow  is 
the  same  as  before.  The  positive  starting  potential  is  in  general  higher 
than  for  the  negative  abrased  and  also  positive  polished  surfaces.  The 


350 


SYLVAN  J.  CROOKER. 


["SECOND 

[SERIES. 


negative  glow  voltage  causes  very  faint  "  spears  "  or  small  brushes  of 
light  to  flash  out  from  sharp  points  here  and  there  on  the  rough  surface. 
These  spears  increase  in  size  and  number  with  increased  potential,  some 
being  much  brighter  than  others.  As  the  potential  is  increased  these 
spears  unite  into  definite,  clear  beads  which  at  times  may  be  very  steady 
and  at  other  times  may  have  more  or  less  violent  lateral  movements.  The 
negative  starting  voltage  for  abraised  surfaces  is  much  smaller  than  for 
the  polished  surfaces. 

At  atmospheric  pressures  the  positive  glow  on  the  abrased  wire  surfaces 
usually  begins  with  a  few  small  flashing  purple  streamers  or  brushes 
extending  from  the  wire  almost  to  the  tube.  These  streamers  are  similar 
in  appearance  to  the  positive  fans  and  streamers  emitted  from  the  surface 
of  the  enamel  covered  wire,  see  Figs.  3  and  4.  These  streamers  increase 
in  brightness  and  are  accompanied  by  soft  glow  as  the  potential  is  in- 
creased. After  a  certain  increase  has  taken  place  in  the  voltage  these 
streamers  disappear  only  the  uniform  glow  remaining  and  increasing  in 
brightness. 

For  the  abrased  negative  wire  at  atmospheric  pressure  the  corona  starts 

SURFACE  CONDITION  AND  DIFFERENT  SIZES  OF  WIRE 


No. 32  Cop 


No. 26  Coppe 
Pressures  7 


No. 20  Cop>er 


P=Poll«he( 

A=Abralsec 


6  7 

KILO">'OLTS 


Fig.  5. 

with  small  flashing  spears  the  same  as  for  the  abrased  wire  at  250  mm. 
These  spears  increase  in  number  very  rapidly  with  an  increase  in  voltage, 
some  of  them  collecting,  so  to  speak,  into  small  bright  beads  and  then 
breaking  up  again.  As  the  potential  is  still  more  increased  the  beads 


]  DIRECT  CURRENT  CORONA.  35 1 

become  more  steady  and  definite,  so  that  at  times  the  abrased  wire  may 
be  covered  with  many  small,  bright,  steady  and  evenly  spaced  beads. 

Chemically  Corroded  Surfaces. — The  positive  visual  corona  for  corroded 
surfaces  is  essentially  the  same  for  all  pressures  as  has  been  described  for 
the  abrased  surfaces.  At  low  pressures  it  begins  with  a  faint  flashing 
glow  which  becomes  steady  and  uniform,  increasing  in  brightness.  At 
pressures  of  250  mm.  the  appearance  is  the  same  as  above,  and  for  at- 
mospheric pressure  the  corona  may  start  with  the  small  purple  brushes 
or  fans  and  an  accompanying  glow,  the  fans  soon  disappearing  and  the 
glow  becoming  uniform  and  increasing  in  brightness.  The  positive 
glow  generally  begins  at  lower  voltages  for  the  corroded  surfaces  than 
for  the  polished. 

The  negative  visual  corona  for  the  corroded  surfaces  is  likewise  similar 
to  that  for  abrased  surfaces  at  the  different  pressures.  Clear  cut  and 
steady  beads  are  obtained  at  the  lower  pressures  but  are  not  as  stable 
for  the  higher  pressures.  In  general  the  negative  starting  voltage  is 
lower  than  for  polished  surfaces. 

III.    CHARACTERISTIC  CURVES  FOR  DIFFERENT  WIRES  AND  SURFACES. 

Varying  the  Radius  of  the  Wire. — The  curves  in  Fig.  5  are  taken  for 
different  sizes  of  copper  wire.  They  show  that  the  effect  of  abrasion  in 
general  lowers  the  starting  point  for  copper  wires  at  atmospheric  pressure. 
The  negative  abrased  curves  are  widely  displaced  from  the  polished  ones, 
showing  that  more  current  flows  in  the  corona  discharge  for  the  same 
voltage  for  wire  abrased  than  for  the  smooth  wire.  The  positive  abrased 
curves  quickly  cross  the  polished  ones  and  then  continue  to  rise  slightly 
displaced,  less  current  flowing  for  the  same  potential  abrased  than  for 
polished.  Thus  the  abrased  surface  has  the  effect  of  restraining  the  flow 
of  the  positive  current. 

The  effect  of  abrasion  is  much  greater  in  the  case  of  the  negative 
current.  The  curves  also  show  that  this  effect  is  greater  for  the  larger 
sizes  of  wire,  which  might  be  expected.  The  higher  starting  potentials 
for  the  larger-sized  wires  is  also  evident. 

The  negative  current  builds  up  very  slowly  at  first  on  the  polished 
surface  but  finally  reaches  a  point  where  it  builds  up  much  faster  than 
the  positive;  at  this  point  the  beads  are  formed.  The  starting  voltage 
for  the  abrased  surface  negative  is  much  lower  than  for  polished  negative. 
The  characteristic  curve  of  the  abrased  wire  is  a  smooth  rising  one 
eventually  crossing  the  polished  negative  curve  for  large  current  values. 
This  same  phenomenon  has  been  observed  for  different  metals. 

Different  Surface  Conditions  for  the  Same  Metal. — Fig.  6  gives  the  char- 


352 


SYLVAN  J.  CROOKER. 


[SECOND 

[SERIES. 


acteristic  positive  and  negative  curves  for  aluminum  wires  at  about 
50  mm.,  showing  the  effect  of  the  three  surface  conditions;  namely, 
polished,  abrased  and  corroded.  The  starting  positive  wire  voltage  for 
the  smooth  surface  is  slightly  lower  than  that  of  the  negative,  but  the 
curves  cross  low,  the  positive  current  building  up  quite  slowly  with  in- 
creased potential,  while  the  negative  curve  is  almost  a  straight  line  rising 


DIFFERENT  SURFACES  FOR  ALUMINUM  WIRE 
Diame.ter  =  0.46  ram. 


Fig.  6. 

very  rapidly.  The  positive  starting  potential  is  higher  for  the  abrased 
surface  than  for  the  polished,  while  that  for  the  negative  abrased  surface  is 
lower.  The  negative  polished  and  abrased  surface  curves  cross  but  the 
positive  do  not.  For  the  corroded  surface  the  positive  glow  voltage  is 
about  the  same  as  for  the  polished  surface,  the  curve  for  the  former  con- 
dition becoming  displaced  shortly,  less  current  flowing  for  the  same 
voltage.  The  negative  starting  potential  is  very  much  lower  in  the  latter 
case  than  that  for  the  polished  surface,  bu  t  crosses  at  a  low  current  value 
and  rises  to  the  right,  less  current  flowing  for  the  same  potential. 

Thus  it  is  seen  that  the  surface  condition  has  a  very  marked  effect  on 
the  starting  point  of  the  corona  as  well  as  on  the  characteristic  curves. 
All  the  wires  were  about  0.41  mm.  in  diameter.  In  general  the  abrased 
surface  has  the  effect  of  lowering  the  starting  potential  for  negative  wire 
and  raising  it  for  positive  wire.  The  starting  point  for  both  positive  and 
negative  in  the  case  of  corroded  wires  is  in  general  lower  than  for  the 
polished  surfaces,  but  the  corroded  surface  characteristics  behave  in 


VOL.  VIII/I 

No.  4. 


DIRECT  CURRENT  CORONA. 


353 


rather  an  erratic  manner,  sometimes  being  displaced  in  one  way  and  some- 
times in  the  opposite. 

Table  II.  gives  a  comparison  between  the  corroded  and  polished  wire 
characteristics  for  both  positive  and  negative  at  different  pressures. 

TABLE  II. 

COMPARING  CORRODED  WITH  POLISHED  WIRE  CHARACTERISTICS. 
Copper. 


Wire. 

Press. 

Starting  Pot. 

Corroded  Surface  Characteristic. 



50.2 

Lower 

Raised. 

+ 

50.4 

ii 

« 

— 

250.0 

<« 

Crosses  high. 

+ 

250.8 

« 

Raised. 

Steel. 


_ 

53.2 

Higher  (press,  diff.) 

Corsses  high. 

+ 

52.4 

Lower 

a         ii 

— 

252.0 

ii 

11      low. 

+ 

252.4 

ii 

Lowered. 

— 

739.4 

ii 

Crosses  high. 

+ 

739.4 

ii 

"       low. 

Aluminum. 


_ 

51.9 

Lower 

Crosses  low.     (For  instance  see 

Fig.  4.) 

+ 

51.9 

ii 

<i         « 

— 

252.0 

« 

midway. 

+ 

252.0 

(i 

Raised. 

— 

745.3 

«< 

Crosses  midway. 

+ 

745.4 

ii 

Raised. 

Silver. 




52.5 

Same 

Lowered. 

+ 

52.5 

Lower 

n 

— 

252.2 

Same 

Crosses  low. 

+ 

252.2 

Lower 

"       midway. 

— 

745.8 

Higher 

Lowered. 

+ 

746.1 

" 

(i 

Different  Metals  of  the  Same  Radius  and  Surface  Condition. — Farwell1 
by  electrolytic  processes  covered  the  surface  of  a  wire  with  different 
metals  to  determine  their  effect.  He  observed  slight  discrepancies  but 
attributed  them  to  experimental  errors  and  concluded  with  Whitehead2 
that  the  formation  of  the  corona  is  independent  of  the  material  of  the  wire. 

Table  I.  compares  the  starting  voltages  for  wires  of  the  same  size  but 

1  S.  P.  Farwell,  "The  Corona  Produced  by  Continuous  Potentials,"  A.  I.  E.  E.f  November 

13.  iQU. 

2  Whitehead,  "The  Electric  Strength  of  Air,  I.,"  A.  I.  E.  E.,  July,  1910. 


354 


SYLVAN  J.  CROOKER. 


[SECOND 
LSERIES. 


of  different  kinds  of  metal  for  different  surfaces  and  pressures.  Curves 
in  Fig.  7  show  a  comparison  between  the  characteristics  of  different 
metals.  Very  marked  differences  are  evident  in  the  characteristic 
curves,  showing  directly  that  the  metal  itself  has  a  part  to  play  in  the 
corona  formation.  The  positive  and  negative  characteristics,  especially 


CHARACTERISTIC  CURVES  FOR  DIFFERENT  METALS 
All  Surfaces  Polished 

Pressure  about  50  mm. 
All     Fe  i  /Ag   i  Cu      t'e  ;A3 


'ti- 
ll 
II 
H 

II 
//J 


3.6 


Fig.  7. 

for  the  case  of  aluminium,  become  widely  separated  for  large  currents, 
the  curves  for  the  other  metals  separate  at  different  rates  for  increasing 
current  values,  but  in  such  a  manner  that  each  metal  behaves  in  its  own 
characteristic  way. 

Slight  differences  in  the  starting  points  for  the  different  metals  were 
noticed;  these  differences  however  are  of  such  a  nature  that  they  cannot 
be  explained  as  being  experimental  errors.  Steel  and  copper  seem  to 
have  about  the  same  starting  point,  while  that  for  aluminum  is  a  little 
higher  and  silver  has  a  value  still  greater.  The  different  metals  not  only 
affect  the  behavior  of  the  characteristic  curves  but  also  the  starting  points 
of  the  corona  glow. 


VOL.  VIII. 
No.  4. 


DIRECT  CURRENT  CORONA. 


355 


The  Effect  of  Ozone  on  the  Corona. — The  presence  of  ozone  has  a  definite 
effect  on  the  appearance  of  the  corona  as  well  as  on  the  characteristic 
curves.  If  ozone  is  present  in  the  corona  tube  in  any  quantity  the 
negative  beads  do  not  form  quite  as  distinctly  as  they  do  when  a  stream  of 
air  is  passing  through  the  tube,  carrying  the  ozone  away.  The  effect 
on  the  negative  characteristic  curve  is  very  slight,  displacing  it  a  little 
to  the  right,  such  that  less  current  can  flow  for  the  same  potential  (see 
Fig.  8).  For  the  positive  characteristic  the  effect  is  somewhat  larger 


THE  EFFECT  OP  OZONE 
Pressure  745  ram. 


1,  wlthou 

2,  with 


Fig.  8. 

and  in  the  opposite  direction,  the  curve  being  displaced  to  the  left,  showing 
that  more  current  for  the  same  potential  flows  through  the  tube  with 
ozone  present  than  does  in  its  absence.  At  atmospheric  pressure  ozone  is 
formed  quite  rapidly  but  its  effect  is  not  large.  At  lower  pressures  with 
less  gas  present  the  formation  of  ozone  is  very  much  less  and  its  effect 
on  the  corona  is  proportionately  smaller. 

The  presence  of  ozone  does  not  explain  the  differences  in  the  character- 
istic curves  for  the  different  metals,  unless  it  is  a  secondary  effect  between 
the  wire  and  the  ozone. 

Formation  of  the  Negative  Beads. — The  formation  and  number  of  the 
negative  beads  depends  not  only  on  the  pressure  and  potential,  but  also 
on  the  surface  condition  and  the  material  of  the  wire.  (See  Farwell  on 
Material  of  Wire.)  Fig.  9  shows  the  relations  between  the  number  of 
beads  and  the  current  for  different  surfaces  of  copper  wire.  The  current 
per  bead  is  larger  for  the  abrased  and  corroded  surfaces  than  for  the 


356 


SYLVAN  J.  CROOKER. 


[SECOND 
[SERIES. 


polished  surface,  assuming  the  whole  current  to  be  carried  by  the  beads. 
For  an  increase  in  pressure  it  is  also  seen  that  the  current  per  bead  is 
much  less,  but  the  beads  are  smaller  in  size.  However,  for  the  higher 
pressures  it  takes  a  larger  voltage  to  produce  the  same  number  of  beads. 
For  the  lower  pressures  the  beads  have  about  the  same  degree  of  stability 


NUMBER  OP  BEADS  AS  A  FUNCTION  OF  THE  CURflENT 
FOR  DIFFERENT  SURFACE  CONDITIONS 
Copper  wire,  0.41  mm.  dia. 


P=  53.8  mm. 
A=  53.2  mm. 
G=  60.2  mm. 


A 


i:  i 


A=  253  ram. 
C=  250  mm. 


20  30.  40 

NUMBER    OF    IEADS 


Fig.  9. 

for  all  the  different  surfaces,  while  for  higher  pressures  the  beads  are  more 
stable  on  the  abrased  or  corroded  surfaces  than  on  the  polished,  it  being 
almost  impossible  to  get  definite  beads  on  the  polished  wire  for  atmospheric 
pressures. 

The  number  of  beads  increases  rapidly  with  increasing  voltage.  Here 
again  the  effect  of  the  materials  is  compared.  For  the  production  of  the 
same  number  of  beads  it  takes  in  general  a  greater  voltage  on  the  steel 
than  on  the  copper  and  aluminum  wires. 

IV.    THEORETICAL. 

Electronic  and  lonization  Effects  Combined. — The  theories  by  Townsend1 
and  Bergen  Davis,2  which  have  been  proposed  to  explain  the  corona  phe- 

1  Townsend,  "A  Theory  of  Glow  Discharges  from  Wires,"  Electrician,  June  6,  1913. 

2  Bergen  Davis,  A.  I.  E.  E.,  April,  1914. 


Na'4]  DIRECT  CURRENT  CORONA.  357 

nomena,  have  been  based  upon  the  assumption  that  only  an  ionization 
of  the  gas  takes  place.  These  theories  have  explained  some  parts  of  the 
observed  phenomena  very  well,  but  as  for  other  parts  it  is  impossible  to 
produce  a  complete  explanation  by  this  one  assumption.  It  is  conceded 
that  the  ionization  effect  has  a  great  deal  to  do  with  the  corona  action 
but  it  is  not  possible  that  there  are  other  effects  which  are  working  in 
conjunction  with  this  one. 

In  the  following  an  attempt  will  be  made  to  explain  the  corona  phe- 
nomena not  as  an  ionization  effect  alone  but  as  a  combined  action  of 
ionization  with  electronic  discharges. 

In  the  experiments  which  have  been  described  on  the  direct  current 
corona  the  striking  difference  between  the  positive  and  negative  corona 
is  everywhere  apparent,  not  only  in  the  visual  corona  but  also  in  the 
characteristic  curves.  The  difference  between  positive  and  negative 
electricity  has  been  noticed  by  many  observers  in  different  experiments. 
For  example,  when  a  metal  is  heated  it  is  known  that  electrons  are 
shot  off,  these  being  negative  charges  of  electricity  which  come  from 
the  metal  itself.  The  same  electronic  discharge  is  obtained  when  a  large 
force  is  acting  between  two  cold  electrodes  in  a  vacuum.  The  example 
is  seen  in  any  X-ray  or  cathode  discharge  tube. 

It  will  make  no  essential  difference  whether  we  assume  the  electrons 
to  come  from  the  metal  itself,  from  the  gas  which  the  metal  has  absorbed, 
or  from  a  thin  layer  of  gas  adhering  to  the  surface  of  the  metal. 

On  the  other  hand  a  discharge  of  positive  electrons  from  a  metal  has 
never  been  observed.  It  always  requires  the  presence  of  a  gas  to  produce 
the  positive  charges  of  electricity.  Experiments  have  also  shown  that 
these  positive  charges  are  atomic  in  size  and  hence  are  to  be  considered 
as  positive  ions. 

The  assumptions  which  are  made  in  this  theory  then,  are  that  there  is  a 
combined  action  of  electronic  discharge  from  the  metallic  surface  along 
with  ionization  in  the  gas.  In  some  cases  the  electrons  will  predominate 
in  determining  the  character  of  the  phenomena,  while  in  others  the  ioniza- 
tion may  be  the  determining  factor. 

Wire  Surfaces  Bare  and  Insulated. — It  might  ordinarily  be  supposed 
that  to  insulate  the  wire  would  increase  the  starting  potential  for  the 
corona  and  cut  down  the  loss.  However,  just  the  reverse  of  this  was 
observed  in  Fig.  3  where  part  of  the  wire  is  covered  with  insulation  and 
part  bare  and  polished.  It  would  seem  almost  like  a  paradox  to  say  that 
insulation  increases  the  corona  loss,  but  it  is  found  possible  to  explain 
this  phenomenon  by  assuming  electronic  discharge  from  the  metal  and 
ionization  in  the  gas. 


358  SYLVAN  J.  CROOKER. 

Fig.  10  represents  the  conditions  in  this  experiment.  A  potential  V 
is  impressed  between  the  wire  and  the  tube. 

RI  =  the  radius  of  the  wire, 

R%  =  the  radius  of  the  insulation,  and 

Rs  =  the  inside  radius  of  the  cylindrical  tube. 

The  electric  force  E  at  the  surface  of  the  wire  which  is  covered  with 
insulation  is  given  by  the  equation, 

Ek2irR  = 


where  k  =  dielectric  constant,  R  =  point  in  which  the  force  is  being 
measured,  and  e  =  charge  on  the  surface  of  the  wire  per  unit  length. 


*•* 


Fig.  10. 
For  a  unit  length  of  the  surface, 

4ire 


To  calculate  the  potential  or  the  work  done  in  carrying  unit  charge  through 
the  distance  dR,  multiply  by  dR, 

2edR 


The  work  done  in  transporting  the  charge  from  RI  to  R%  is 

f*  2e   rR*dR      2^      Rz 

EdR  =  T  I      •«•  =  Y  log-p-  .  (2) 

JBl  k  JMl    R        k        RI 

Similarly,  the  work  done  through  the  distance  RZ  to  RS,  where  k  =  I  ,  is 


The  potential 

f*2  C*3  1 1  ,     ^2  ^3  \ 

V  =          EdR  +          EdR  =  2e\-  log^-  +  log-^-  I  ,  (4) 

JjRi  JRZ  \#         &l  &*' 

T7 

(5) 


,  , 


No^4VI11']  DIRECT  CURRENT  CORONA.  359 

The  capacity  when  the  wire  is  insulated  is  readily  calculated  since, 

e  I 

s7) 


Then  when  air  only  is  the  intervening  medium,  k  =  I  and  Rz  =  RI, 
therefore, 

Ci=~  Sr  (8) 

,         ^3 

2log=- 

•Kl 

and  from  (5), 


By  comparing  (7)  and  (8)  it  is  seen  that  the  capacity  is  increased  by 
placing  insulation  on  the  wire  and  we  can  therefore  conclude  that  with 
the  same  potential  difference  the  charge  e  on  the  surface  will  also  be 
increased. 

The  force  necessary  to  draw  unit  electric  charge  out  from  the  metal 
when  it  is  insulated  is  expressed  by  the  relation 


but 


then 

F  = 
and  from  (5) 

72 


I_        Rz  Rs\* 


therefore 

F2 


Since  the  insulation  is  very  thin  R%  is  very  nearly  equal  to  RI,  and 

approximately  and  (n)  becomes, 

F-  V* 


360  SYLVAN  J.  CROOKER. 

When  there  is  no  insulation  on  the  wire,  R%  =  RI  and  only  air  remains 
between  the  electrodes,  k  =  I,  and  (n)  reduces  to, 

V2 

Fl  =  ~ 


F  and  FI  differ  only  by  the  constant  i/k  so  it  is  easily  seen  that  the 
force  F  necessary  to  pull  the  electrons  from  the  wire  surface  which  is 
covered  with  insulation  is  much  smaller  than  FI,  the  force  necessary  to 
draw  the  electrons  from  the  free  surface  after  the  insulation  has  become 
punctured.  Therefore  when  the  wire  is  negative,  as  is  the  case  in  No.  14, 
Fig.  3,  there  will  be  glow  on  the  insulated  side  appearing  at  points  where 
the  insulation  has  broken  down  and  there  will  be  no  glow  on  the  polished 
surface.  The  discharge  in  this  case  is  essentially  electronic,  the  spots  of 
light  which  appear  are  intensely  bright  and  the  potential  at  which  glow 
begins  is  very  much  lower  than  when  the  wire  is  positive. 

When  the  wire  is  charged  positively  as  in  Fig.  3,  No.  15,  there  appears 
a  faint  uniform  glow  on  the  polished  surface.  This  is  the  characteristic 
positive  glow  which  has  a  pale  blue  color.  This  may  be  explained  as  being 
essentially  an  ionization  effect.  That  is,  the  wire  being  charged  to  a 
certain  positive  value  has  force  enough  to  split  up  the  gas  molecules  by 
collisions  in  its  immediate  neighborhood  and  when  the  energy  is  large 
enough  light  is  emitted.  The  negative  particles  are  attracted  to  the  wire 
while  a  layer  of  positive  ions  collect  at  the  wire  surface. 

On  the  enameled  end  of  the  wire  the  density  of  electricity  is  larger  per 
unit  length.  The  streamers  or  fans  of  purple  light  approach  the  ap- 
pearance of  the  direct  current  arc  both  in  form  and  color,  so  we  might 
say  that  these  streamers  are  negative  ions  moving  toward  the  positive 
wire  with  a  great  velocity.  An  analogy  to  this  brush  discharge  phenom- 
enon would  be  the  stream  lines  of  air  entering  small  holes  in  a  pipe 
carrying  vacuum.  The  particles  of  air  which  are  drawn  to  the  pipe  with 
increasing  velocity  are  analogous  to  the  negative  ions  which  are  drawn 
to  the  wire  with  velocity  increasing  as  the  wire  is  approached.  These 
purple  brushes  have  been  noticed  at  different  times  for  bare  wires  when 
positively  charged.  They  seem  to  come  especially  from  irregularities 
or  points  on  the  wire  where  there  would  be  a  great  surface  density. 

The  starting  potential  for  corroded  surfaces  has  in  general  been  found 
to  be  much  lower  than  for  polished  surfaces.  An  explanation  is  easily 
found  by  considering  either  one  of  two  effects.  Either  the  size  of  the 
wire  is  slightly  reduced  by  corrosion,  enabling  the  corona  to  start  at 
lower  voltages  or  the  corroded  surface  acts  as  an  insulator  giving  the  same 


No%yiIL]  DIRECT  CURRENT  CORONA.  361 

condition  as  has  been  explained  for  the  phenomena  in  Fig.  3.  The  dif- 
ference in  starting  potentials  for  corroded  and  polished  surfaces  is  in 
general  so  large  that  the  former  explanation  is  hardly  feasible,  since  the 
size  of  the  wire  could  not  have  been  greatly  reduced.  The  latter  seems 
to  give  the  best  explanation,  since  it  is  known  that  most  of  the  oxides 
when  dry  are  good  insulators,  and  it  would  be  possible  with  such  an  in- 
sulating layer  to  get  a  large  difference  in  the  starting  potentials. 

The  Negative  Beads. — The  negative  beads  may  be  considered  as  being 
unstable  in  two  senses.  First,  they  move  back  and  forth  along  the  length 
of  the  wire,  and,  second,  they  give  rise  to  oscillations.  For  instance  it  is 
known  that  a  gas  column  or  stream  of  electrons  as  in  the  Poulson  arc  is 
very  unstable  and  gives  rise  to  high  frequency  oscillations. 

At  the  very  beginning  of  the  negative  corona  the  glow  covers  the  whole 
wire.  A  certain  amount  of  energy  is  stored  up  in  this  layer  which  is  in  an 
unstable  condition  and  easily  breaks  up  into  the  characteristic  beads. 
This  is  similar  to  a  film  of  water  covering  a  wire  or  string.  The  film  will 
be  uniform  until  a  certain  point  of  instability  is  reached  when  it  will  break 
up  into  drops  or  beads.  This  breaking  up  of  an  original  uniform  layer 
into  beads  has  been  observed  over  and  over  again.  As  soon  as  a  bead 
is  formed  a  large  current  starts  in  that  region  which  heats  the  gas  and 
the  metal  at  that  point.  A  thin  metal  wire  may  easily  melt.  If  the 
temperature  rises  and  the  potential  difference  decreases  at  these  points, 
the  metal  will  be  oxidized  and  the  discharge  will  take  place  at  a  different 
point,  causing  the  beads  to  move  backward  and  forward  along  the  wire. 

Moreover  the  beads  assume  the  shape  of  a  fan  whose  plane  is  perpen- 
dicular to  the  wire,  so  that  in  these  planes  the  temperature  will  be  higher 
than  in  the  neighboring  regions.  This  will  give  rise  to  an  unstable  tem- 
perature distribution  which  will  cause  the  beads  to  move  along  the  wire. 
This  effect  is  more  pronounced  when  the  wire  is  in  a  vertical  position. 

This  instability  is  also  shown  by  the  fact  that  the  pressure  increase 
due  to  ionization  when  the  wire  is  negative  is  very  erratic  and  cannot  be 
measured  accurately,  and  by  the  fact  that  the  field  in  the  tube  cannot  be 
investigated  by  a  third  sounding-electrode,  since  very  irregular  results 
are  obtained  due  to  the  presence  of  the  beads,  while  the  positive  wire 
gives  very  regular  results  which  can  easily  be  repeated  and  show  a  marked 
distortion  of  the  field  between  the  wire  and  the  cylinder. 

There  are  several  other  cases  in  which  the  negative  elctricity  escapes 
from  surfaces;  for  instance,  in  the  mercury  arc  the  glow  from  the  negative 
terminal  does  not  come  from  the  whole  surface  of  the  electrode  but  from 
a  bright  spot  on  the  surface  of  the  mercury  which  moves  about  irregularly. 
Another  case  would  be  that  of  the  ordinary  carbon  arc  under  certain 


362  SYLVAN  J.  CROOKER. 

conditions  when  the  negative  end  of  the  flame  moves  about,  and  still 
another,  Dr.  Knipp's  cylindrical  cathode.1  Indeed  the  negative  bead 
resembles  the  arc  in  several  respects;  it  may  be  called  a  small  arc  which 
by  increasing  the  voltage  gradually  goes  over  into  the  more  definite  arc. 

The  beads  represent  in  the  second  place  a  more  or  less  unstable  dis- 
charge in  so  far  as  oscillations  are  very  easily  set  up.  S.  P.  Farwell  has 
shown  that  a  small  spark  gap  in  series  with  the  corona  tube  gives  rise  to 
oscillations  in  the  electric  circuit.  Bennett2  has  shown  that  oscillations 
arise  readily  in  the  negative  part  of  the  corona  for  alternating  currents. 
The  arc,  for  instance  the  Poulson  arc,  is  a  transformer  of  direct  current 
into  alternating  current  of  a  very  high  frequency. 

The  beads  are  always  brighter  and  steadier  at  low  pressures  that  at  high 
pressures.  At  low  pressures  the  electronic  discharge  from  the  metal 
predominates  over  the  ionization  by  collision  in  the  gas.  With  increasing 
pressure  the  ionization  by  collision  becomes  more  and  more  important, 
the  beads  become  smaller  and  more  numerous. 

For  a  certain  pressure  and  potential  difference  beads  will  appear  on 
the  abrased,  polished  and  corroded  surfaces  of  a  steel  wire  in  exactly 
the  same  way  (see  fig.  2,  Nos.  6  and  9).  This  happens  between  the  pres- 
sures of  30  and  40  mm.  At  a  lower  pressure  (25  mm.)  and  a  smaller 
potential  difference  beads  appear  only  on  the  polished  part,  while  a  more 
or  less  uniform  glow  covers  the  corroded  and  the  abrased  portions;  the 
surface  irregularities  on  the  corroded  and  abrased  parts  giving  rise  to 
very  many  overlapping  beads,  forming  a  soft  glow.  There  are,  as  it 
were,  too  many  but  too  weak  opportunities  for  the  formation  of  well- 
defined  beads.  For  still  lower  pressures  and  potential  differences  the 
original  glow  covers  only  the  polished  portion  first  and  it  is  only  on  that 
part  that  the  clear  beads  will  form. 

Returning  to  the  pressure,  30  to  40  mm.,  where  the  beads  are  evenly 
distributed  over  the  whole  wire,  and  increasing  the  pressure  and  the 
potential  difference,  then  the  number  of  beads  increases.  They  become 
unsteady  and  fuzzy  especially  along  the  corroded  and  polished  parts  and 
finally  with  still  higher  pressures  the  beads  are  only  well  defined  on  the 
abrased  part,  where  they  probably  are  fixed  by  rough  surface  irregular- 
ities which  act  like  small  lightning  rods.  During  all  of  these  changes  of 
the  negative  corona  the  positive  glow  remains  perfectly  constant,  forming 
a  well-defined  uniform  bluish  glow  along  the  wire. 

It  has  already  been  shown  that  one  should  expect  for  corroded  surfaces 
a  smaller  starting  voltage  than  for  the  polished  wire  for  both  polarities. 

1  Dr.  C.  T.  Knipp,  Science,  May,  1916. 

2  Bennett,  Trans.  A.  I.  E.  E.,  Vol.  32  (1913)- 


N?L'4VIJ1']  DIRECT  CURRENT  CORONA.  363 

For  the  negative  abrased  wire  the  starting  voltage  also  is  smaller  than 
for  the  negative  polished  wire,  a  result  which  is  evident.  As  clear  beads 
are  formed  for  the  abrased  wire  at  higher  pressures  one  should  expect  that 
the  negative  characteristic  curve  is  higher  than  that  for  the  polished 
wire  and  that  is  actually  the  case  (see  Fig.  2,  No.  8,  and  Fig.  5).  On  the 
other  hand  if  at  low  pressures  bright  beads  are  formed  on  the  polished 
wire  one  should  expect  the  current  to  be  larger  than  for  the  abrased  and 
corroded  wire  and  this  also  is  the  case.  (Compare  Fig.  2,  No.  4,  and  Fig. 
6.)  Bright  beads  are  always  accompanied  by  a  large  current.  Corrosion 
and  abrasion  have  little  influence  on  the  positive  characteristics. 

CONCLUSIONS. 

1.  The  surface  conditions  as  well  as  the  metal  itself  has  an  effect  on 
the  starting  voltage  and  on  the  characteristic  curves. 

2.  The  number  and  brightness  of  the  negative  beads  depend  in  a  very 
complicated  way  on  the  surface  conditions. 

3.  A  thin  layer  of  insulation  on  the  wire  renders  the  escape  of  negative 
electricity  easier.     This  paradox  has  been  explained. 

4.  The  formation  of  beads  and  their  instability  has  been  explained  on 
the  assumption  that  the  current  is  due  to  an  emission  of  electrons  from 
the  surface  of  the  metals  and  due  to  ionization  by  collision.     Most  of 
the  complicated  phenomena  have  been  explained  by  this  assumption. 

An  expression  of  thanks  must  be  given  to  Prof.  A.  P.  Carman  through 
whose  kindness  facilities  for  these  experiments  were  provided,  and  to 
Dr.  Jakob  Kunz,  whose  suggestions  and  assistance  have  proven  a  constant 
source  of  help  throughout  the  work. 

LABORATORY  OF  PHYSICS, 

UNIVERSITY  OF  ILLINOIS, 
URBANA,  ILLINOIS, 
May  15,  1916. 


[Reprinted  jrom  SCITSSCE,  N.  S. ,   Vol.  XLIX., 
1271,  Pages  450-451,  May  9,  1919] 


TO  CUT  OFF  LARGE  TUBES  OF  PYREX  GLASS 

ON  a  number  of  occasions  I  have  heard  the 
remark  from  instructors  in  physics  and  chem- 
istry, who  do  most  of  their  own  glass  blowing, 
that  they  are  unable  to  "  cut "  off  squarely 
large  tubes  of  pyrex  glass.  Small  tubes,  up  to 
about  20  mm.  in  diameter,  yield  readily  to  the 
usual  file  mark. 

A  well-known  method  for  cutting  large  tubes 
of  common  glass  is  to  make  a  file  scratch 
round  the  tube,  apply  one  turn  of  an  iron  wire 
held  taut,  and  then  heat  the  same  to  redness 
by  an  electric  current. 

This  method,  however,  without  modification, 
fails  when  attempting  to  cut  pyrex  tubes. 
The  glass  will  simply  not  crack,  and  if  the 
heating  is  pushed  the  hot  wire  usually  sinks 
into  the  glass  and  finally  fuses  under  the 
intense  heat. 

I  was  surprised  recently  to  find  that  if  the 
iron  wire  is  replaced  by  a  nichrome  wire,  say, 
of  no.  14  or  16  gauge,  the  tube  may  be  cut  off 
by  the  incandescent  wire  in  the  same  manner 
that  a  cake  of  soap  is  cut  in  two  parts  by 
means  of  a  string. 

To  insure  success  proceed  as  follows:  Take 
a  length  of  about  one  foot  of  nichrome 
wire,  connect  it  up  to  a  D.  0.  (or  A.  C.)  dy- 
namo current  and  include  an  adjustable  tin 
resistance  (for  the  current  required  must  nec- 
essarily be  large).  The  wire  is  held  under 
tension  by  pulling  on  it  with  a  pair  of  pincers, 
as  shown  in  Fig.  1.  Care  must  be  taken  not 
to  let  the  two  parts  of  the  wire  touch  at  A. 
When  all  is  in  readiness,  turn  on  the  heating 
current  and  adjust  same  by  means  of  the  tin 


resistance  until  the  wire  glows  a  white  heat. 
If  now  a  blast  from  a  hand  torch  be  allowed 
to  play  on  the  wire  and  glass  the  tube  may  be 
cut  as  shown  in  Fig.  2.  Be  careful  not  to  let 
the  flame  strike  the  glowing  wire  where  it 
is  not  in  contact  with  the  glass  for  the  extra 
heat  will  burn  it.  The  object  of  the  blast  is 


to  aid  in  softening  the  glass,  and  also  to  dis- 
tribute the  heat  along  the  tube  and  thus  pre- 
vent the  freshly  cut  edges  from  checking  due 
to  the  otherwise  intense  local  heating.  The 
burr  of  glass  that  results  from  the  cutting 
may  be  removed  by  a  file  or  on  the  grindstone. 

Recently  the  neck  of  a  twelve-liter  pyrex 
Florence  flask  was  cut  off  with  the  greatest 
ease.  The  diameter  was  about  60  mm.,  and 
the  wall  thickness  about  2.5  mm. 

CHAS.  T.  KNIPP 

UNIVERSITY  or  ILLINOIS 


(Reprinted  from  the  PHYSICAL  REVIEW,  N.  S.,  Vol.  IX,  No.  3.  March  1917.] 


TOLMAN'S    TRANSFORMATION    EQUATIONS,    THE    PHOTO- 
ELECTRIC EFFECT  AND   RADIATION   PRESSURE. 


BY  S.  KARRER. 


R 


C.  TOLMAN  uses  the  following  transformation  equations  when 
applying  his  principle  of  similitude, 

/'  =  */;     t'  =  xt\    er  =  e]    m'  =  m/x\     S'  =  5. 


P.  W.  Bridgman  has  pointed  out  that  these  equations  are  a  particular 
case  out  of  a  large  number  of  possible  transformations  which  follow  from 
the  principle  of  dimensional  homogeneity.  Tolman  has  shown  that,  in 
many  instances,  the  application  of  the  above  equations  leads  to  results 
in  accord  with  experiment.  We  wish  to  point  out  two  important  cases 
where  the  transformation  equations  give  results  which  are  in  accord  with 
present  knowledge. 

In  the  first  place,  let  us  assume  we  know  from  experiment  that  the 
kinetic  energy  E  of  the  electrons  emitted  from  a  metal  under  the  influence 
of  light,  minus  a  constant  EQ  is  only  a  function  f(n)  of  the  frequency  n 
of  the  incident  light,  and  is  independent  of  the  intensity  of  the  light  and 
of  the  temperature  and  special  properties  of  the  metal.  That  is,  assume 

E  -  EQ  =  /(n). 
Then  from  the  equations  above  it  follows  that 

77    /  0  J  /  ^ 

x  ~  x' 

E'-E0'=/(n'), 

E  -  EQ 


x  being  arbitrary,  this  functional  equation  must  hold  for  every  value  of  x. 
Its  solution  will  be  of  the  form, 

/(»)  =  hn, 
where  h  is  a  constant,  hence 

E  -  EQ  =  hn, 


29  1  5.  KARRER. 

which  is  Einstein's  photoelectric  equation,  h  must  be  determined  by 
experiment;  the  measurements  of  Millikan  give  strong  support  to  the 
correctness  of  this  equation.  And  further,  his  results  show  that  h  is 
identical  with  Planck's  radiation  constant.  From  Tolman's  point  of 
view  this  is  a  very  interesting  result,  but  from  the  standpoint  of  Bridgman 
it  is  a  necessary  condition  that  the  application  of  Tolman's  equations 
give  a  correct  result. 

It  is  important  to  notice  that  Tolman's  equations  do  not  give  any 
definite  result  in  the  case  of  the  relation  between  the  photoelectric  current 
and  the  intensity  of  the  light  incident  on  the  metal. 

In  the  second  place,  we  will  apply  the  transformation  equations  to  get 
the  relation  between  the  pressure  exerted  upon  a  body  by  the  radiation 
incident  upon  it  and  the  density  of  the  radiation.  Assume,  experiment 
shows  that  the  pressure  p  depends  only  on  the  energy  density  E  of  the 
radiation,  then  p  =  f(E),  and  since 

-W:',-.  .:,  f-t     and     E'=f, 

/(E)  must  satisfy  the  following  functional  equation, 


That  is 

p  =  /(£)  =  HE, 

where  k  is  a  constant.    As  is  well  known,  experiment  shows  that  the 
radiation  pressure  is  proportional  to  the  energy  density  of  the  radiation. 

SUMMARY. 

Tolman's  transformation  equations  lead  to  Einstein's  law  of  the 
photoelectric  effect  if  it  is  assumed  that  the  kinetic  energy  of  the  electrons 
emitted  from  a  metal,  minus  a  certain  constant,  is  only  dependent  upon 
the  frequency  of  the  incident  light. 

The  equations  also  lead  to  the  correct  relation  between  the  pressure  of 
radiation  and  the  density  of  the  radiation. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
January,  1917. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  IX.,  No.  3,  March,  1917.] 


AN    IMPROVED   HIGH   VACUUM    MERCURY  VAPOR   PUMP. 

BY  CHAS.  T.  KNIPP. 

"^HE  diffusion  pump  of  Gaede1  has  stimulated  a  number  of  investi- 
-^-  gators  in  this  country  to  enter  the  field  of  pump  design  with  the  result 
that  several  improvements  involving  new  principles 
have  been  published.  In  a  recent  number  of  the  PHYS- 
ICAL  REVIEW  Langmuir2  describes  an  improved  mer- 
cury vapor  pump  "characterized  by  its  extreme  speed 
and  the  high  degree  of  vacuum  attainable."  The  wri- 
ter of  this  note  being  interested  for  a  number  of  years 

in  the  production  of  high  vacua  also  seized  upon    ^ 1_ 

this  opportunity  to  aid,  if  possible,  in  simplifying  the 
means  by  which  vacua  are  produced  in  the  research 
laboratory  and  submits  the  following  design  made 
wholly  of  glass  as  an  improved  high-vacuum  high- 
speed mercury  vapor  pump. 

The  pump  complete,  except  the  usual  mercury 
vapor  trap,  is  shown  in  the  figure,  which  is  one  third 
full  size.  The  bulb  to  be  exhausted  and  trap  are 
fused  to  B,  while  the  tube  E  is  attached  to  the  sup- 
porting  or  rough  pump.  The  mercury  vapor  rising 
from  the  lower  bulb,  which  is  heated  in  a  sand  or 
heavy  oil  bath,  streams  up  through  the  short  tubes 
P  and  0  and  is  deflected  downward  through  an  an- 
nular throat  by  the  umbrella  N.  The  issuing  mer- 
cury vapor  at  once  condenses  on  the  water-cooled 
surface  of  the  enveloping  tube  and,  as  Langmuir3 
pointed  out,  the  gas  that  comes  from  B  is  forced 
mechanically  downward  from  the  lower  edge  of  N 
along  the  cooled  surface  of  the  condensing  chamber. 
This  accumulated  gas  is  removed  through  the  lat- 
eral tubes  b  b,  which  unite  at  the  top  and  form  the  vacuum  mercury  vapor 
exhaust  tube  E,  all  being  enveloped  by  the  water  p 
jacket  XY,  as  shown  in  the  figure.  This  construction  keeps  the 

1  Ann.  Physik,  46,  357,  1915- 

1  PHYS.  REV.,  8,  48,  July,  1916. 

1  Gen.  Elect.  Rev.,  19,  1060,  Dec.,  1916. 


An 


Fig.  1. 
improved     high 


312  CHAS.   T.   KNIPP. 

mercury,  which  collects  at  the  ring-seal  3,  cool,  and  thus  removes  the 
objection  that  mercury  vapor  having  an  upward  velocity  would  enter 
the  annular  condensing  chamber.  A  small  opening  shown  at  3  serves 
as  a  valve  which  allows  the  accumulated  mercury  to  pass,  yet  due  to 
surface  tension  maintains  a  perfect  seal.  The  short  tube  P  is  inserted 
to  shield  the  hot  mercury  vapor  streaming  up  from  the  boiler  from 
condensing  on  the  surfaces  at  3.  The  upper  end  of  P  telescopes  loosely 
into  the  lower  end  of  0,  while  the  lower  end  is  secured  by  the  ring-seal  I , 
having  also  a  small  valve  opening  in  it  through  which  the  mercury  passes 
back  into  the  boiler.  By  making  the  upper  end  of  P  conical  condensed 
mercury  vapor  is  caught  in  the  annular  space  thus  formed  and  auto- 
matically seals  the  space  PO  from  the  cavity  just  outside  of  P.  The 
cold  mercury  collected  at  the  ring-seal  3,  and  the  adjacent  water-jacket, 
thus  have  but  little  opportunity  of  cooling  the  hot  stream  of  mercury 
vapor  passing  up  through  PO,  and,  furthermore,  the  temperature  gradient 
between  the  ring-seals  I  and  2,  and  3  and  b  b  are  not  abrupt,  hence  there 
is  no  danger  of  the  glass  cracking.  This  construction  very  much  simplifies 
the  glass-blowing,  since  the  tube  throughout  the  process  is  kept  perfectly 
symmetrical. 

In  the  absence  of  a  convenient  means  of  measuring  the  pressure 
within  the  discharge  vessel  quickly,  the  writer  has  chosen  to  express 
the  degree  of  exhaustion  in  terms  of  the  cathode  dark  space  and  the 
sparking  distance  at  a  parallel  gap  in  air.  The  induction  coil  used  was 
a  10  cm.  spark  Kohl  coil,  and  the  parallel  gap  was  between  balls  1.75 
cm.  in  diameter.  The  supporting  pump  was  a  Gaede  rotary  mercury 
pump  backed  by  a  Gaede  oil  box  pump.  The  mercury  was  heated  in  an 
oil  bath  by  one  bunsen  burner.  The  trap  beyond  B  was  immersed  in 
liquid  air.  Mercury  vapor  pumps  are  not  sensibly  operative  until  the 
vacuum  drawn  by  the  supporting  pump  is  of  the  order  of  I  cm.  Crookes 
dark  space,  depending  upon  the  construction  of  the  pump  as  regards 
annular  throat,  etc.  Hence  the  test  for  speed  should  not  be  from 
atmospheric  pressure.  The  following  tests  serve  to  give  an  indication 
of  the  speed  attainable. 

Test  i. — With  the  discharge  vessel  fused  to  B  (through  a  centimeter 
tube  30  cm.  long)  having  a  volume  of  270  c.c.  it  required,  by  repeated 
trial,  29  minutes  to  lengthen  the  dark  space  from  I  cm.  to  5  cm.  equivalent 
spark  in  air;  while  with  the  mercury  vapor  pump  operative  it  required 
but  43  seconds. 

Test  2. — With  a  6  liter  vessel  attached  by  a  short  large-diameter  tube, 
it  required  51  minutes  to  range  from  I  cm.  dark  space  to  an  equivalent 
parallel  gap  in  air  of  4.65  cm.;  which  time  interval  with  this  pump 


No!"4*X']  HIGH    VACUUM   MERCURY    VAPOR  PUMP.  313 

operative  was  reduced  to  2%  minutes.  At  the  end  of  another  2  minutes 
the  vacuum  was  so  hard  that  the  10  cm.  Kohl  coil  was  not  able  to  force 
a  discharge. 

The  advantages  of  this  form  of  hot  blast  mercury  vapor  condensation 
glass  pump  may  be  briefly  stated  as 

1.  The  symmetrical  design  simplifies  the  glass-blowing. 

2.  Full  effectiveness  of  the  hot  blast  of  mercury  vapor  without  sensible 

loss  of  heat  through  a  long  delivery  tube. 

3.  Effective  cooling  by  a  proper  placing  of  water-jacket,  ring-seals,  and 

of  an  internal  shielding  tube. 

4.  The  use  of  simple  mercury  valves  for  the  direct  return  of  the  con- 

densed mercury  vapor  to  the  boiler. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
January  15,  1917. 


Reprinted  from  Vol.  XVII,  No.  5,  May,  1917,  School 
Science  and  Mathematics. 


A  SIMPLE  DEMONSTRATION  TUBE  FOR  EXHIBITING  THE 
MERCURY  HAMMER,  GLOW  BY  MERCURY  FRICTION, 
AND  THE  VAPORIZATION  OF  MERCURY  AT  REDUCED 
PRESSURE.1 

BY  CHARLES  T.  KNIPP, 
University  of  Illinois,  Urbana. 

When  the  pressure  over  mercury  is  reduced  to  that  of  mercury 
vapor  only,  vaporization  with  heat  takes  place  at  surprisingly 
low  temperatures,  and  the  resulting  mechanical  pressure 
exerted  by  the  issuing  vapor  from  the  mercury  surface  is  even 
more  surprising.  The  magnitude  of  this  pressure  over  a  sur- 
face confined  in  a  large  bulb,  so  that  the  vapor  stream  is  not  con- 
centrated, is  sufficient  even  at  temperatures  as  low  as  130°  C. 
to  freely  support  bits  of  cork.  To  make  this  easy  of  demonstra- 
tion the  writer  has  designed  a  tube  to  show  the  above,  together 
with  the  familiar  mercury  hammer,  and  glow  by  mercury  fric- 
tion phenomena — all  in  one. 

1  Apparatus  exhibited  and  demonstrated  before  the  Galesburg  meeting  of  the  Illinois  Acad- 
emy of  Science,  February  24,  1917. 


MERCURY  EXPERIMENTS 


443 


The  tube  should  be  about  35  cm.  long  by  l^cm.  in  diameter, 
and  have  the  usual  bulb  at  each  end  that  obtains 
for  the  mercury  hammer.  A  stricture  reducing 
the  diameter  to  y£  cm.  is  placed  near  one  end. 
A  small  quantity  of  mercury  (about  10  grams) 
is  put  in  the  tube,  and  also  a  spherical  pith  ball 
about  y^  cm.  in  diameter  is  placed  in  the  bulb 
farthest  removed  from  the  stricture.  The  tube  is 
pumped  out  carefully  and  sealed  off  (the  sealing- 
off  nipple  should  be  attached  to  the  stem  and  not  to 
one  of  the  bulbs) .  It  is  now  ready  for  the  exhibition 
of  the  three  phenomena  referred  to  above.  To 
show  the  pressure  of  the  mercury  vapor  it  is  only 
necessary  to  hold  the  tube  by  the  upper  bulb  (the 
one  farthest  from  the  stricture)  over  a  Bunsen 
burner  and  allow  it  to  heat  gently.  Soon  con- 
densed mercury  vapor  appears  on  the  walls  of 
the  lower  bulb  and  its  progress  up  the  tube  is 
readily  followed.  The  bombardment  of  the  mercury 
vapor  lifts  the  pith  ball  which,  oscillating  up  and 
down,  is  forced  into  the  upper  bulb  where  it  is 
violently  agitated  by  the  expanding  mercury  vapor 
stream.  Removing  the  apparatus  from  the  heat 
allows  the  oscillating  pith  ball  to  descend  the  tube 
until  it  again  rests  upon  the  stricture.  At  this 
moment  if  the  bulb  is  returned  to  the  flame  th% 
ball  is  again  almost  instantly  shot  upward — 
showing  in  a  striking  manner  how  sensitive  the  apparatus  is. 
There  is  little  danger  of  cracking  the  tube  if  care  is  taken  not  to 
plunge  the  lower  bulb  suddenly  into  the  flame,  and  if  it  is  allowed 
to  cool  before  laying  down. 

The  other  two  phenomena,  i.  e.,  the  mercury  hammer,  and 
glow  by  mercury  friction,  are  so  familiar  that  they  do  not  call 
for  special  mention  here. 


DISTRIBUTION  OF  POTENTIAL  IN  A  CORONA  TUBE. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  X,  No.  3,  September,  1917.] 


DISTRIBUTION  OF   POTENTIAL   IN  A   CORONA  TUBE. 

BY  HARRY  T.  BOOTH. 

I.     INTRODUCTION. 

I.  General  Characteristics  of  D.-C.  Corona. — The  name  corona  has  been 
applied  collectively  to  the  conduction  phenomena  appearing  when  a 
sufficiently  high  potential  difference  is  applied  to  two  electrodes  (two 
parallel  wires,  or  two  coaxial  cylinders)  separated  by  a  gas.  Corona 
appears  for  both  alternating  and  direct  impressed  potential  differences; 
for  the  purpose  of  our  investigation,  however,  di- 
rect current  corona  was  the  more  suitable. 

Since  a  knowledge  of  the  distribution  of  poten- 
tial between  the  electrodes  will  be  necessary  for 
any  fundamental  corona  theory,  an  investigation 
has  been  carried  out  at  this  laboratory  to  deter- 
mine the  field  at  every  point  between  a  wire  and  a 
coaxial  tube,  under  various  conditions  of  impressed 
Fig.  a.  voltage,  pressure,  size  of  wire,  and  current.  It  is 

hoped  that  the  data  taken  will  aid  in  the  formu- 
lation of  an  adequate  corona  theory. 

II.     METHOD. 

The  distribution  of  potential  between  a  wire  and  a  coaxial  cylinder 
was  investigated  in  the  following  manner. 

A  hole  was  drilled  in  the  side  of  a  cylinder,  and  an  insulated  wire  ter- 
minating in  a  bare  spherical  tip  was  arranged  so  that  it  could  be  moved 
radially  between  the  wire  and  the  tube.  A  micrometer  microscope  di- 
rected on  a  fixed  point  of  the  movable  wire  served  to  determine  the 
relative  position  of  the  point.  An  electrostatic  voltmeter  of  small 
capacity  was  connected  in  series  with  the  exploring  point  and  the  tube. 

When  the  point  was  moved  to  any  portion  of  the  radial  field,  the  volt- 
meter quickly  showed  a  constant  deflection,  indicating  that  the  potential 
of  the  point  was  in  equilibrium  with  that  of  the  field  at  that  particular 
place. 

By  moving  the  exploring  point  from  the  tube  to  the  wire,  observing 
the  voltmeter  readings  at  certain  intervals,  a  comparatively  accurate 
estimate  of  the  intensity  of  the  field  was  obtained. 


NoL'3X']  DISTRIBUTION  OF  POTENTIAL  IN  A  CORONA   TUBE.  26  J 

III.    APPARATUS. 

1 .  The  Corona  Tube. — The  corona  tube  as  indicated  in  the  accompany- 
ing sketch  was  35.5  cm.  long  and  7  cm.  in  diameter.     The  central  wire 
was  of  copper,  well  polished,  and  stretched  tightly.     In  all,  four  wires 
were  used,  No.  40,  No.  32,  No.  28  and  No.  20  B.  &  S.  gauge. 

The  ends  of  the  tube  were  covered  with  heavy  plate  glass,  drilled  for 
the  central  wire,  and  sealed  fast  with  half  and  half  wax. 

Since  it  was  necessary  to  work  at  pressures  lower  than  atmospheric,  a 
glass  tube  was  sealed  over  the  exploring  rod,  so  arranged  with  ground 
joints  and  springs  as  to  allow  the  point  to  be  moved  at  will  without 
destroying  the  constant  pressure. 

2.  Source  of  Potential. — The  source  of  continuous  potentials  used  in 
this  set  of  investigations  consisted  of  a  battery  of  40  500  volt,  0.5  ampere, 
shunt-wound,  D.-C.  generators  connected  in  series. 

These  were  arranged  so  that  the  potential  could  be  varied  continuously 
from  about  300  volts  up  to  20,000  volts.  Power  for  the  driving  motors 
was  supplied  by  a  motor  generator  set  equipped  with  a  voltage  regulator, 
so  that  the  voltage  variation  on  the  no-volt  power  line  was  constant  to 
within  less  than  .5  per  cent. 

In  general,  the  potential  of  the  high  tension  line  was  as  constant  as 
the  accuracy  of  the  work  demanded. 

3.  Voltmeters. — For  the  measurement  of  voltages,   three  voltmeters 
were  used,  a  Kelvin  electrostatic  voltmeter  with  three  ranges,  a  Braun 
electrostatic  voltmeter,  and  a  General  Electric  electrometer  type  volt- 
meter. 

These  instruments  were  calibrated  with  an  attracted  disc  electrometer, 
equipped  with  a  scale  and  vernier  so  that  the  distance  between  plates 
could  be  read  to  0.05  mm.  The  force  on  the  disc  was  measured  by  a  fine 
balance. 

The  Braun  voltmeter  had  a  range  of  0-3,500  volts,  and  since  it  is 
essentially  an  electroscope,  it  was  almost  ideal  for  use  with  an  exploring 
point. 

The  Kelvin  instrument  had  3  ranges,  0-5000,  2,000-10,000,  and  4,000- 
20,000  volts. 

4.  Current  Measurements. — Currents  between  the  wire  and  the  tube 
were  measured  by  means  of  a  D'Arsonval  galvanometer,  used  in  connec- 
tion with  an  Ayrton  universal  shunt.    The  figure  of  merit  of  the  galvanom- 
eter was   obtained,  using   standard    resistances  and    a  dry  cell  whose 
E.M.F.  had  been  determined  by  comparison  with  a  standard  cell. 


268 


HARRY  T.  BOOTH. 
TABLE  OF  CURVES. 


FSECOND 

[SERIES. 


Figure 

Curve. 

Wire 
B&  S 
Gauge. 

Voltage. 

/Amperes. 

PMm. 
of  Hg. 

Temp. 
°C. 

Remarks. 

1 

1 

20 

12,500 

9.76.  10-* 

745 

25° 

Faint  glow 

2 

20 

13,850 

6.62.10-5 

745 

25° 

Good  glow 

3 

20 

15,420 

1.6  .10-4 

745 

25° 

Good  glow 

4 

20 

16,000 

1.78.10-4 

745 

25° 

Good  glow 

2 

1 

20 

1,450 

3.9  .10-6 

23.5 

27° 

Dull  glow 

2 

20 

2,150 

2.31.10"4 

23.5 

27° 

Bright  glow 

3 

20 

2,950 

5.58.10-4 

23.5 

27° 

Brilliant  purple  glow 

4 

20 

2,150 

Electrostatic  curve 

3 

1 

20 

10,000 

9.  23.10-5 

450 

27° 

3  or  4  steady  beads 

wire  negative 

4 

1 

28 

8,400 

3.19.10-6 

745 

25° 

No  apparent  glow 

2 

28 

10,200 

2.66.  10-* 

745 

25° 

Faint  glow 

3 

28 

11,500 

7.1  .10-* 

745 

25° 

Dull  glow 

4 

28 

13,450 

1.95.10-4 

745 

25° 

Good  glow 

5 

28 

14,000 

3.73.10-4 

745 

25° 

Bright  glow 

5 

1 

28 

1,520 

4.43.10-6 

19 

24° 

Good  glow 

2 

28 

1,750 

1.35.10-4 

19 

24° 

Good  glow 

3 

28 

2,320 

3.73.10-4 

19 

24° 

Bright  glow 

4 

28 

2,890 

6.92.10-4 

19 

24° 

Brilliant  glow 

5 

28 

2,320 

Electros 

:atic  cur 

ve 

6 

1 

28 

1,800 

9.48.10-4 

19 

24° 

About  30  steady  beads 

7 

I 

32 

6,510 

4.17.10-8 

747 

25° 

No  glow 

2 

32 

6,825 

1.91.  10-6 

747 

26° 

Distinct  glow 

3 

32 

7,425 

1.91  10-5 

747 

26° 

Good  glow 

4 

32 

8,400 

5.94.10-5 

747 

26° 

Good  glow 

5 

32 

9,900 

9.54.10-6 

747 

26° 

Bright  glow 

8 

1 

32 

6,825 

1.91.  10-6 

747 

26° 

Distinct  glow 

2 

32 

6,825 

2.03.10-4 

241 

24° 

Bright  glow 

3 

32 

6,825 

3.46.10-4 

885 

24° 

Brilliant  glow 

4 

32 

6,825 

Electrostatic  curve 

-  9 

1 

32 

5,050 

1.79.10-8 

744 

26° 

No  glow 

2 

32 

5,650 

2.39.  10-6 

744 

26° 

A  few  dull  beads 

3 

32 

7,250 

3.10.10-6 

744 

26° 

Beads  1  cm.  apart 

10 

1 

40 

4,520 

4.77.10-8 

740 

22° 

No  glow 

2 

40 

4,700 

1.19.10-6 

740 

22° 

Distinct  glow 

3 

40 

6,500 

2.  26.  10-* 

740 

22° 

Good  glow 

4 

40 

8,400 

8.29.10-6 

740 

22° 

Good  glow 

5 

40 

9,900 

1.67.10-4 

740 

22° 

Brilliant  glow 

6 

40 

8,400 

Electrostatic  curve 

VOL.  X.l 
No.  3.   J 


DISTRIBUTION  OF  POTENTIAL  IN  A  CORONA   TUBE. 


269 


IV.     RESULTS. 

i.  General  Type  of  Curves. — By  the  method  of  exploration  already 
described,  curves  for  the  distribution  of  potential  between  wire  and  tube 
were  taken  for  No.  40,  No.  32,  No.  28  and  No.  20  copper  wires  stretched 
along  the  axes  of  the  tube.  These  curves  were  taken  for  various  pressures 
and  voltages  after  the  appearance  of  the  corona.  Representative  curves 
obtained  are  shown  in  Figs.  I  to  10,  and  the  conditions  under  which  each 
curve  was  taken  are  given  in  Table  I. 

For  the  No.  40  wire,  it  was  found  impossible  to  obtain  curves  of  the 


\\ 


V 


\ 


\ 


jz 


f 


Fig.  1. 


Fig.  2. 


potential  distribution  when  the  wire  was  negative;  for  a  given  position 
of  the  exploring  point  the  readings  of  the  voltmeter  were  not  constant. 
The  beads  appearing  when  the  wire  is  negative  were  seldom  at  rest,  and 
this  would  lead  to  the  conclusion  that  each  movement  of  the  beads  is 
accompanied  by  a  change  in  the  field  surrounding  the  wire. 

For  No.  32  wire,  when  the  wire  was  negative,  two  curves  shown  in  Fig.  9 


I 


\V 


\ 


Fig.  3. 


Fig.  4. 


were  taken  before  the  corona  appeared,  also  a  portion  of  a  curve  for  a 
voltage  at  which  there  was  a  distinct  series  of  beads  along  the  wire. 

Curves  were  also  obtained  for  No.  28  and  No.  20  wire  when  the  wires 
were  negative,  the  same  general  characteristics  being  exhibited  in  each. 

3.  Discussion  of  Curves. — The  corona  discharge  in  general  is  divided 


270 


HARRY  T.  BOOTH. 


[SECOND 

[SERIES. 


into  two  classes,  according  as  (i)  the  wire  is  positive,  and  (2)  the  wire  is 
negative. 

The  first  case,  when  the  wire  is  positive,  is  characterized  by  a  uniform 


\ 


I 


\ 


Fig.  5. 


Fig.  6. 


purplish  glow  around  the  wire.     The  second  case,  however,  differs  in 
appearance.     When  the  potential  is  sufficiently  high,  small  tufted  beads 


\\ 


\ 


\ 


Fig.  7. 


Fig.  8. 


appear  on  the  negative  wire,  and  are  at  rest  only  under  exceptional 
conditions. 

Curves  are  shown  for  both  positive  and  negative  wires.     Let  us  con- 


i   i 


i 


Fig.  9. 

sider  the  appearance  of  the  potential  distribution  curves  when  the  wire 
is  positive. 


Na's']  DISTRIBUTION  OF  POTENTIAL  IN  A  CORONA   TUBE.  2J I 

i.  The  Positive  Wire. 

In  general,  the  space  between  the  anode  and  the  cathode  may  be  broken 
up  into  four  regions. 

1.  A  region  immediately  surrounding  the  wire,  which  is  characterized 
by  a  very  large  potential  gradient.     This  may  be  due  to  the  excess  of 
the  number' of  ions  or  electrons  approaching  the  electrode  over  the 
number  of  those  leaving,  since  the  former  number  includes  ions  generated 
at  all  parts  of  the  field,  whereas  the  latter  contain  only  ions  that  are 
generated  in  the  narrow  layer  close  to  the  wire.     Thus  we  can  see  that 
the  charges  on  the  excess  of  negative  ions  near  the  wire  disturb  the  electric 
field  so  that  the  potential  difference  per  centimeter,  or  the  gradient,  is 
large  near  the  surface  of  the  wire. 

2.  A   region    of   approximately   constant   force   extending   from    the 
"  surface  layer  "  region  adjacent  to  the  wire,  to  a  point  which  varies 
with  the  pressure,  current,  and  voltage.     At  the  higher  voltages,  the 
actual  potential  at  a  given  point  in  this  region  is  greater  than  the  the- 
oretical electrostatic  potential,  and  the  tangent  to  the  curve  may  be 
either  greater  or  less.     Figs.  2  and  5  show  the  electrostatic  curve  (dotted), 
in  comparison  with  actual  curves  taken. 

3.  A  region  of  little  or  no  force  near  the  tube.     In  passing  from  II.  to 
III.  the  number  of  positive  ions  increases  (since  they  are  generated  in  all 
the  space  between  the  wire  and  region  III.),  and  their  charges  oppose 
those  on  the  negative  ions  to  such  a  degree  that  not  only  the  negative 
charges  on  the  ions,  but  also  the  electrostatic  forces  due  to  the    con- 
figuration of  the  system  are  neutralized. 

4.  A  region  close  to  the  tube,  corresponding  to  the  "  surface  layer  " 
contiguous  to  the  wire.     In  this  space,  positive  charges  accumulated  at 
all  the  remaining  parts  of  the  radial  field  are  predominant,  and  three  is 
an  abrupt  cathode  drop  at  the  surface  of  the  tube. 

2.  Wire  Negative. 

When  the  wire  is  negative  and  corona  appears,  a  potential  curve  is 
obtained  which  differs  somewhat  from  the  positive  curves.  Large 
cathode  and  anode  drops  appear,  and  the  intervening  space  has  a  very 
small  field.  Reasoning  similar  to  that  explaining  the  shape  of  the  curves 
when  the  wire  is  positive  explains  the  negative  curves. 

So  in  general,  the  anode  and  cathode  drops  of  potential  are  predominant 
in  both  types  of  curves.  There  are  several  reasons  for  this,  namely: 

1 .  Polarization  potential  between  a  metal  and  a  gas. 

2.  Accumulation  of  ions. 

3.  Reflection  of  ions. 


272  HARRY  T.  BOOTH. 

4.  Different  velocities  of  positive  and  negative  ions. 

5.  A  non-uniform  field. 

The  Potential  Curves  from  a  Theoretical  Point  of  View. 
I.  The  starting  point  of  the  corona. 
We  have  Peeks  empirical  formula  for  the  starting  intensity, 


where  EI  is  the  force  at  the  surface  of  the  wire  of  radius  RI  and  £0  and 
/3  are  constants. 

From  the  general  electrostatic  theory,  at  the  moment  when  the  corona 
discharge  is  starting,  just  before  the  field  has  been  disturbed  by  the  moving 
charges, 


Therefore  at  the  instant  when  the  corona  starts 


or 

(f.  -r.)       i 

:.  ••;.-     *+•-«*,,*•          <4) 

which  resembles  the  general  formula  for  the  electric  force  between  two 
concentric  cylinders, 

£=>.  (5) 


Hence,  when  r  =  7?i  + 


2.  Calculation  of  the  volume  density  of  electrification  in  the  space 
between  the  two  concentric  cylinders. 

For  a  system  where  the  potential  at  a  point  is  due  to  moving  charges 
as  well  as  static  charges,  we  have  Poisson's  equation  expressing  the 
density  in  terms  of  the  potential, 

V2F  =  -  47rp,  (6) 

or,  writing  it  in  cylindrical  coordinates, 

d2V      i  dV       i  d2F      d*V 


VOL.  X.I 
No.  3.   J 


DISTRIBUTION  OF  POTENTIAL  IN  A   CORONA   TUBE. 


273 


For  this  particular  case,  the  derivatives  in  z  and  <£  are  zero,  so  rewriting 
the  above  equation,  using  total  derivatives, 

d?V      idV 
dr  +  r  dr 


=     —   47T/7. 


(8) 


Since  the  density  is  an  undetermined  function  of  the  radius,  the  equa- 
tion cannot  be  integrated  directly.  If,  however,  we  plot  the  potential 
against  the  distance  from  the  axis,  a  graphical  method  will  aid  in  the 
determination  of  the  density.  That  is,  if  the  first  derivative  of  the 
potential  is  determined  from  the  curve  for  a  series  of  values  of  r,  these 
new  values  may  be  plotted  against  the  radius  again.  By  repeating  this 
process  with  the  derived  curve,  a  relation  between  the  second  space 
derivative  and  the  radius  is  obtained.  From  these  two  derived  curves, 
then,  the  density  may  be  computed  according  to  equation  (8). 

Fig.  ii  is  a  repetition  of  Curve  4,  Fig.  I,  and  Fig.  12  shows  the  density 
as  computed  for  the  different  values  of  r. 

The  density  curve  shows  what  we  have  deduced  intuitively  in  regard 


I 


Fig.  11. 


Fig.  12. 


to  the  charges  necessary  to  produce  the  observed  distortion  of  the  field. 
The  large  resultant  negative  charge  near  the  positive  wire  and  the  positive 
charge  near  the  negative  tube  should  be  expected.  A  peculiar  maximum 
appears  at  about  2.7  cm.  from  the  wire  (Fig.  12). 

4.  Sources  of  Error. 

i.  Potential  assumed  by  a  sphere  in  an  ionized  gas. 

It  is  difficult  to  draw  conclusions  as  to  the  absolute  potential  of  a  sphere 
in  a  conducting  gas,  since  it  is  very  likely  that  the  potential  at  an  undis- 
turbed point  in  a  gas  is  not  the  same  as  the  potential  assumed  by  a  sphere 
when  its  center  is  at  this  point. 

In  the  case  of  a  sphere  near  the  positive  electrode,  its  potential  being 
initially  the  same  as  that  of  the  gas,  two  streams  of  ions  move  in  opposite 
directions  past  the  side  of  the  sphere,  one  containing  a  large  number  of 


274  HARRY   T.   BOOTH. 

negative  ions,  and  the  other  a  smaller  number  of  positive  ions.  It 
intercepts  more  negative  ions  than  positive,  so  that  its  potential  falls 
below  that  of  the  surrounding  gas.  The  charge  thus  acquired  by  the 
sphere  increases  until  the  effect  which  it  produces  in  attracting  positive 
and  repelling  negative  ions  causes  them  to  come  in  contact  with  the 
sphere  in  equal  numbers.  The  final  value  of  the  potential  assumed  by 
the  sphere  is  too  high  by  an  amount  which  depends  upon  the  relative 
velocities  of  the  positive  and  negative  ions. 

Conversely,  when  the  exploring  sphere  is  close  to  the  negative  electrode, 
there  are  a  greater  number  of  positive  ions  intercepted  than  negative  ions, 
so  that  the  potential  of  the  sphere  rises  above  the  potential  of  the  undis- 
turbed gas,  until  finally  an  equilibrium  is  reached,  the  number  of  positive 
charges  acquired  by  the  sphere  being  equal  to  the  number  of  negative 
charges.  Thus  the  potential  assumed  by  the  sphere  is  greater  than  that 
of  the  undisturbed  gas. 

If,  however,  the  velocity  of  the  positive  ions  is  approximately  equal 
to  that  of  the  negative  ions,  then  the  exploring  point  should  attain  very 
nearly  the  same  potential  as  that  of  the  surrounding  gas.  For  the 
pressures  used  in  this  series  of  experiments,  the  velocities  of  the  ions  are 
nearly  the  same.  Thus  the  error  introduced  could  not  have  been  very 
great. 

A  slight  error  might  be  introduced  if  there  was  an  appreciable  voltmeter 
leakage  between  the  point  and  the-power  line.  The  shape  of  the  point 
also  affects  the  shape  of  the  potential  curve  to  a  small  degree.  The  volt- 
meters used  were  practically  free  from  leakage,  and  the  work  was  done 
during  cold,  dry  weather,  so  the  error  introduced  from  this  cause  is  neg- 
ligible. 

An  attempt  is  being  made  to  formulate  the  mathematical  theory  of  the 
corona  discharge,  and  it  is  hoped  that  these  potential  curves  will  aid  in  the 
solution  of  the  problem. 

Summary. — The  distribution  of  potential  between  the  electrodes  of  a 
corona  tube  was  determined  for  four  sizes  of  wire,  for  various  pressures 
and  potential  differences.  From  these  curves  the  density  of  the  charge 
along  the  radius  was  derived  by  means  of  graphical  methods. 

In  conclusion,  I  wish  to  express  my  appreciation  of  the  suggestions  and 
advice  given  by  Dr.  Jakob  Kunz,  of  this  laboratory,  and  to  Mr.  J.  W. 
Davis  and  Mr.  R.  W.  Owens  for  the  use  of  portions  of  their  data  on  this 
problem. 

PHYSICS  LABORATORY, 

UNIVERSITY  OF  ILLINOIS, 
May  n,  1917. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  X,  No.  5,  November,  1917.] 


THE  PRESSURE  INCREASE  IN  THE  CORONA. 

BY  EARLE  H.  WARNER. 

I.     INTRODUCTION. 

IT  has  been  reported  by  Farwell  and  Kunz  that  at  the  instant  the 
corona  appears  about  an  axial  wire  in  a  cylindrical  tube,  the  pressure 
of  the  gas  in  the  tube  suddenly  increases.1  It  has  always  been  stated 
that  this  pressure  increase  could  not  be  due  to  heat,  because  of  the  in- 
stantaneous character  of  its  appearance,  and  because  of  the  rapidity 
with  which  it  disappears  as  soon  as  the  potential  is  removed  from  the 
wire.  Since  the  only  theories  which  have  been  advanced  to  explain 
the  corona  assume  it  to  be  an  ionization  phenomenon,  it  seemed  reason- 
able to  suppose  that  this  pressure  increase  was  due  to  the  increase  in  the 
number  of  gas  particles  in  the  tube,  and  so  it  was  called  ionization  pres- 
sure. Experiments  have  been  performed  and  reported2  which  show  that 
this  pressure  increase  is  exactly  proportional  to  the  corona  current,  with 
the  wire  positive  when  dry  air,  hydrogen,  nitrogen,  carbon  dioxide, 
oxygen  and  ammonia  are  the  gases  in  the  tube.  Since  the  publication 
of  this  data  Arnold3  has  contended  that  the  pressure  increase  could  be 
completely  accounted  for  as  the  result  of  Joule's  heat,  and  that  the 
assumption  that  it  is  due  to  ionization  is  untenable.  To  support  this 
contention  Arnold  performed  experiments  "  by  electrically  heating  the 
central  wire  in  apparatus  similar  to  Farwell's  and  "  observed  the  pressure 
increase.  With  such  an  apparatus  Arnold  attempted  to  show  (i)  that 
an  increase  in  pressure  due  to  heat  appears  suddenly,  (2)  that  for  a  given 
power  consumed  in  the  tube  the  increase  in  pressure  due  to  heat  is  of 
about  "  the  same  magnitude  as  those  observed  "  in  the  corona. 

In  order  to  show  clearly  that  the  pressure  increase  is  not  due  to  heat 
a  series  of  comparative  experiments  were  performed  with  the  pressure 
increase  caused,  first,  by  producing  the  corona  glow  on  the  wire  and, 
second,  by  heating  the  central  wire.  The  pressure  increase  observed  in 
the  first  set  of  experiments  will  be  referred  to  as  caused  by  corona  and  in 
the  second  set  as  caused  by  heat. 

1  Dr.  S.  P.  Farwell,  "The  Corona  Produced  by  Continuous  Potentials,"  Proc.  A.  I.  E   E. 
Nov.,  1914.     Dr.  Jakob  Kunz,  "On  the  Initial  Condition  of  the  Corona  Discharge,"  PHYS. 
REV.,  July,  1916. 

2  Earle  H.  Warner,  "  Deterjnination  of  the  Laws  Relating   Ionization  Pressure  to  the 
Current  in  the  Corona  of  Constant  Potentials,"  PHYS.  REV.,  Sept.,  1916. 

»H.  D.  Arnold,  (Abstract)  PHYS.  REV.,  Jan.,  1917. 


484 


EARLE  H.   WARNER. 


[SECOND 

[SERIES. 


Pressure  Increase 
Due  To  Heat. 


1.75 


A  few  computations  have  also  been  made  which  strengthen  the  results 
of  the  experiments. 

II.     EXPERIMENTAL  RESULTS. 

1.  The  reason  why  one  who  sees  this  pressure  increase,  as  recorded  by 
a  quick-acting  pressure  meter,  thinks  it  is  not  a  heat  effect,  is  because  of 
rapidity  with  which  it  appears  and  disappears.     Arnold  showed  that  the 
pressure  increase  occurred  quite  rapidly  when  caused  by  heat.     The 
following  curves  show  the  difference  in  the  rapidity  of  appearance  and 
disappearance  of  the  pressure  increase  caused  by  heat,  and  caused  by 
corona.     It  will  be  noticed  in  Fig.  I,  where  the  pressure  increase  was 

caused  by  heating  the  central  wire,  that 
fifteen  seconds  was  required  for  the 
prssure  to  come  to  its  maximum  value, 
and  that  from  the  time  the  current  was 
broken  twenty-five  seconds  was  required 
for  the  pressure  to  return  to  practically 
its  original  value,  while  in  Fig.  2,  where 
the  pressure  increase  was  caused  by  co- 
rona, only  three  seconds  was  required 
for  the  maximum  pressure  to  be  at- 
tained and  that  the  pressure  came  back 
to  practically  its  original  value  in  eigh- 
teen seconds.  In  this  last  case  from  the 
appearance  of  the  phenomenon  it  seems,  if  the  aneroid  pressure  me- 
ter had  less  inertia,  that  the  pressure  increase  could  be  determined  in 
less  than  three  seconds.  These  curves  show  that  the 
pressure  increase  appears  five  times  as  rapidly  when 
caused  by  corona  as  when  caused  by  heat,  and  disap- 
pears also  more  rapidly. 

2.  In  the  pressure  increase  due  to  corona,  a  short 
time  interval  of  five  to  seven  seconds  occurs  after  the 
sudden  increase  of  pressure,  before  the  heat  effect  in 
the  corona  begins  to  be  noticed.     This  is  shown  by  an 
abrupt  bend,  A,  in  the  curve  where  the  pressure  in- 
crease is  plotted  against  time,  as  is  done  in  Fig.  3. 
No  such  bend  occurs  in  the  case  where  the  pressure 

increase  is  caused  by  heat  alone,  as  is  shown  in  Fig.  i .  In  the  work  which 
has  previously  been  reported  the  pressure  increase  measurements  were 
always  taken  at  the  point  A ,  and  this  seems  to  be  practically  independent 
of  the  heat  effect. 


20   30   4o   50 

Time  in  Seconds. 


Fig.  1. 


Pressure  Increase 
Due  To  Corona. 


Fig.  2. 


VOL.  X.I 
No.  5-  J 


THE  PRESSURE  INCREASE  IN  THE  CORONA. 


485 


3.  The  heat  which  is  produced  in  the  corona  discharge,  shown  by  the 
gradual  pressure  increase  from  B  to  C,  Fig.  3,  is  distributed  throughout  the 
whole  volume  of  enclosed  air  and  so,  when  the  current  is  broken  does  not 
radiate  rapidly  because  the  air  is  a  poor  conductor.  This  is  shown  very 
clearly  in  Fig.  4.  This  seems  to  show  that  the  pressure  increase  due  to 


Pressure  Increase  Due  To  Corona. 


1.75 


2.00 
1.75 


!°.75 

0.25 

&' 


Pressure  Increase  Due  To  Corona. 


10   20   30   40   50   60    70 
Time  in  Seconds. 


20   40   60   60   100   120   140   160  ISO  200 
Time  in  Seconds. 


Fig.  3. 


Fig.  4. 


heat  in  the  corona  is  represented  by  the  difference  of  ordinates  of  C  and 
B  (Fig.  4).  As  soon  as  the  corona  current  is  broken  at  C  the  increase 
in  pressure  due  to  corona  at  once  disappears,  but  the  increase  in  pressure 
due  to  heat  in  the  corona  discharge  remains,  as  is  shown  by  the  difference 
of  ordinates  of  D  and  A .  This  difference  is  always  very  nearly  equal  to 
the  difference  of  ordinates  of  C  and  B.  This  heat  energy  produced  by 
the  corona  current,  since  it  is  distributed  through  the  gas,  radiates  very 
slowly,  as  is  shown  by  the  gradual  descent  of  the  curve  from  D  to  E. 
No  such  effect  is  observed  when  the  increase  of  pressure  is  due  entirely 
to  heat,  as  is  shown  in  Fig.  i.  This  curve  (Fig.  i)  shows  that  twenty-five 
seconds  after  the  current  through  the  wire  is  broken  at  C  the  resultant 
pressure  increase  due  to  heat  has  practically  disappeared;  while  Fig.  4 
shows  that  twenty-five  seconds  after  the  corona  is  removed  from  the  wire 
the  increase  in  pressure  due  to  the  corona  has  disappeared,  but  practically 
all  the  pressure  increase  due  to  heat  in  the  corona  (ordinates  C  minus  B 
approximately  equals  ordinates  D  minus  A]  still  remains  and  radiates 
very  slowly. 

4.  If  the  increase  in  pressure  is  due  to  heat,  the  same  increase  in 
pressure  should  result  when  the  same  power  is  consumed  (a)  with  a 
corona  current  through  the  gas,  (b)  with  a  heating  current  through  the 
wire.  Figs.  5  and  6  show  that  this  is  not  the  case.  The  powers  con- 
sumed in  the  two  cases  are  not  exactly  the  same,  but  one  can  see  that  were 
they  the  same,  the  increase  in  pressure  due  to  corona  would  be  approxi- 


486 


EARLE  H.  WARNER. 


[SECOND 
[SERIES. 


mately  one  half  the  increase  in  pressure  due  to  heat.  The  power  in  the 
case  of  the  corona  was  obtained  by  multiplying  the  potential  difference 
between  the  wire  and  the  tube  by  the  corona  current,  and  in  the  case  of 


£  1    nn 

0 

•0.75 

7 

0 

•H  0.50 

/ 

r  |  m 

|  0.25 

p 

~epsu 
Due. 
0.5 

-e  In 
To  H 
>3S  W 

;reae< 

sat. 
itts 

'    NU-4- 

10   20   30   40   50   60   70 

Time  in  Seconds. 


Fig.  5. 


Fig.  6. 


the  heated  wire  was  obtained  by  multiplying  the  current  through  the 
wire  by  the  potential  difference  across  that  portion  of  the  wire  which  was 
in  the  tube. 

5.  If  the  increase  in  pressure  in  the  corona  discharge  is  due  to  heat  the 
temperature  of  the  air  in  the  corona  tube  must  increase.     This  may  or 
may  not  be  the  case  in  the  luminous  layer  near  the  wire  but  the  tem- 
perature of  the  gas  in  the  tube  at  a  point  four  millimeters  from  the  wire 
actually  decreases.     This  was  determined  by  inserting  a  sensitive  ther- 
mocouple made  of  very  fine  Copper-Advance  wire  into  the  corona  tube. 
The  temperature  decreased  only  at  the  instant  the  corona  appeared.     In 
a  short  time,  after  the  heat  due  to  the  corona  began  to  appear  (corre- 
sponding to  the  slope  B  to  C,  Figs.  3  and  4)  the  temperature  of  the  gas 
in  the  tube  began  to  increase.     This  cooling  effect  is  shown  in  Fig.  7. 
Comparing  Figs.  7  and  3  it  is  seen  that  the  increase  in  pressure  which 

was  measured  at  A  was  observed  while  there 
was  an  actual  cooling  in  the  corona  tube. 
This  cooling  should  be  expected  when  air  or 
oxygen  are  in  the  tube,  for  under  these  condi- 
tions ozone  is  formed.  Since  the  formation  of 
ozone  from  oxygen  is  always  accompanied  with 
an  absorption  of  heat  the  temperature  of  the 
air  or  oxygen  would  tend  to  lower.  Mr.  J. 
W.  Davis,  working  on  corona  about  hot  wires 
in  hydrogen,  has  discovered  that  the  appearance  of  the  corona  about  a 
tungsten  wire  heated  to  white  heat,  causes  it  to  cool  to  dull  red.  This 
tends  to  show  that  even  in  the  corona  glow  itself  there  is  a  cooling  effect. 

6.  If  the  increase  in  pressure  in  the  corona  is  due  to  heat  one  should 
expect  it  to  be  the  same  with  the  wire  either  positive  or  negative.     As 
has  been  previously  mentioned  it  is  impossible  to  obtain  measurements 


it 

*J;H  Cooling  Effect  in  Corona, 


Ei 

lo     37 

4J           , 

Tim 
1 

&  in  Sec. 
0       20        1 

3 

/ 

Decrease  Lr 
Galvanome 

VJ  V*  V 
•£•  Vfl  ( 

( 

/ 

X^l 

^^ 

Fig.  7. 


THE  PRESSURE  INCREASE  IN  THE  CORONA.          487 

when  the  wire  is  negative  because  of  the  presence  of  beads.     The  negative 
corona  is  entirely  different  from  the  positive  corona. 

7.  The  following  consideration  will  further  show  that  the  increase  in 
pressure  can  not  be  due  to  heat.  The  heat  produced  by  the  corona 
current  will  be  given  by  the  equation  H  =  0.238  eit  and,  if  the  observed 
pressure  increase  is  due  to  heat,  the  increase  in  pressure  Lp  will  be  pro- 
portional to  the  heat,  and  we  can  write  A£  =  k  eit.  Now  the  only  way 
for  A£  to  vary  directly  as  i,  the  corona  current,  as  is  the  case — shown  by 
curves  in  the  last  article — is  for  e  to  be  independent  of  i.  Data  shows  that 
this  is  not  the  case. 

III.    RESULTS  FROM  THEORETICAL  CONSIDERATIONS. 

1.  If  the  increase  in  pressure  is  due  to  heat  it  is  possible  to  compute 
the  magnitude  of  the  pressure  increase  when  one  knows  the  watts  of 
electrical  energy  consumed  in  the  tube.     The  trial  represented  in  Fig.  6 
gives  us  this  data.     The  observed  pressure  increase  was  measured  in 
three  seconds  so  that  the  total  number  of  joules  of  work  consumed  by 
the  tube  in  that  time  was  3  X  0.266  =  0.798  joules  and  this  corresponds 
to  0.1909  calories.     Knowing  the  volume  of  the  tube,  the  temperature 
and  pressure  of  the  air  in  it,  the  mass  of  the  air  in  the  tube  can  be  com- 
puted.    With  the  above-mentioned  quantity  of  heat  and  mass  of  air, 
together  with  the  specific  heat  of  the  air  at  constant  volume,  the  temper- 
ature rise  of  the  air  can  be  computed,  assuming  that  the  electrical  energy 
is  converted  into  heat.     This  temperature  rise  comes  out  to  be  2.44°  C., 
which  at  constant  volume  corresponds  to  a  pressure  increase  of  about 
nine  cm.  of  water,  while  the  observed  pressure  increase  in  this  particular 
trial  amounts  to  about  seven  tenths  cm.  of  water.     In  this  computation 
radiation  and  conduction  losses  have  been  neglected  because  they  would 
be  very  small  from  a  body  2.44°  C.  above  room  temperature.     This 
shows  that  the  observed  results  lie  in  a  different  order  of  magnitude  from 
what  would  be  expected  if  Arnold's  theory  were  true. 

2.  Arnold  states,  if  "we  compute  the  corona  currents  that  would 
result  from  the  presence  of  enough  ionized  particles  to  produce  the  ob- 
served pressure  changes,  the  currents  calculated  are  many  thousand  times 
greater  than  those  actually  obtained."     Such  a  statement  is  only  true 
when  the  ionized  particles  are  produced  in  a  uniform  or  practically  uni- 
form electric  field.     This  is  not  the  case  in  the  corona  tube.     H.  T.  Booth 
is  publishing  data  on  the  distortion  of  the  field  in  the  corona  tube.     This 
data  shows  that  the  potential  gradient  near  the  wire  is  very  high — of  the 
order  of  30,000  volts  per  cm.     This  is  the  arcing  gradient,  in  which  it  is 
probable  every  molecule  is  ionized.     Then  for  a  long  space  between  the 


488 


EARLE  H.  WARNER. 


[SECOND 

[SERIES, 


0.600 


1400 


Current  As  a  Function  of  Pressure    / 
Constant  Voltage          |  / 
Hydrogen.  / 

*4 


wire  and  the  tube  there  is  a  very  small  gradient.  With  this  condition 
of  the  field,  near  the  wire  every  molecule  may  be  ionized  and  still  the 
resultant  current  be  very  small,  for  few  of  the  ionized  particles  near  the 
wire  will  pass  through  the  space  where  there  is  a  small  gradient.  Simple 

I8on  _         computations  based  on  kinetic 

theory  show  that  the  maximum 
observed  pressure  increases  can 
be  explained  by  ionization  if 
every  molecule  of  the  air  with- 
in 1.39  mm.  of  the  wire  is 
ionized.  Within  this  distance 
the  potential  gradient  is  equal 
to  the  arcing  gradient  and 
therefore  probable  that  all  mole- 
cules are  ionized. 

IV.     FURTHER  VERIFICATION 

OF  KUNZ'S  THEORY. 
The    final  equation   as   pre- 
sented in  the  last  article  is 

ki  =  —  (pi  —  po)  +  a  constant, 

6 

where  i  is  the  corona  current, 
VQ  the  volume  of  the  tube,  e 
the  potential  difference  between 
the  wire  and  the  tube,  pi  —  po 
the  pressure  increase,  k  a  con- 
stant and  po  the  initial  pressure.  This  equation  shows  that  for  a  con- 
stant potential  difference  e,  the  current  i  should  increase  as  po  is  low- 
ered. Data  were  taken,  by  measuring  the  current  at  various  measured 
pressures,  caused  by  a  constant  potential  difference,  which  verifies  this 
theory.  These  data  are  shown  graphically  in  Figs.  8  and  9  when  pure 
hydrogen  and  nitrogen  respectively  were  the  gases  in  the  tube. 


Fig.  8. 


V.  SUMMARY  AND  CONCLUSIONS. 

Experimental  results  show: 

1.  That  the  increase  in  pressure  due  to  corona  appears  and  disappears 
much  more  rapidly  than  when  due  simply  to  heat. 

2.  That  the  heat  in  the  corona  discharge  is  not  a  prominent  factor 
until  many  seconds  after  the  corona  appears. 


VOL.  X.l 
No.  s-  J 


THE  PRESSURE  INCREASE  IN  THE  CORONA. 


3.  That  in  equal  energy  experiments  the  increase  in  pressure  due  to 
corona  differs  from  the  increase  in  pressure  due  to  heat  by  about  50  per 
cent. 

4.  That  at  the  instant  the  corona  appears  the  gas  in  the  tube  at  a 
small  distance  from  the  wire  is  cooled. 


600 


200 


Current  As  a  function  of  Pressure. 

Constant  Voltage 

Hitrogen 

Wire  + 


7620 

77 


720 


680      640      600 

Pressure  in  Mm.  of  Mercury. 


560 


520 


Fig.  9. 

5.  That  the  theory  advanced  by  Kunz  is  verified  in  one  more  field, 
namely  in  the  relation  between  current  and  pressure  for  constant  voltage. 

These  results  together  with  conclusions  drawn  from  simple  calculations, 
force  one  to  believe  that  the  pressure  increase  in  the  corona  discharge  is 
not  due  to  Joule's  heat.  With  the  recent  knowledge  of  the  distortion  of 
the  field  in  the  corona  tube  it  seems  very  possible  that  the  increase  in 
pressure  is  due  to  ionization. 

The  writer  desires  to  express  his  appreciation  to  Professor  A.  P.  Carman 
for  the  use  of  the  laboratory  facilities,  and  to  Dr.  Jakob  Kunz  for  his 
continued  interest  and  suggestions. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
June,  1917. 


Reprinted  troin  the  PHYSICAL  REVIEW.  N.a..  Vol.  XII,  No    i.  July,  1918.] 


ON  BOHR'S  ATOM  AND  MAGNETISM. 

BY  JAKOB  KUNZ. 

pHERE  are  two  outstanding  problems  in  the  field  of  physics  at 
the  present  time,  the  problem  of  the  nature  of  light  and  its  origin 
and  the  problem  of  magnetism.  Light  and  magnetism  seem  to  be  very 
directly  connected  with  electrical  charges  in  motion  and  the  ultimate 
theory  of  the  origin  of  light  may  involve  the  solution  of  the  problem  of 
magnetism.  Several  attempts  have  been  made  at  an  explanation  of  the 
radiation  of  the  black  body  and  of  the  emission  of  line  spectra.  The 
most  surprising  fact  that  has  been  brought  to  light  by  these  investiga- 
tions is  the  existence  of  the  quantum  constant  h,  which  seems  to  belong 
to  the  fundamental  constants  of  nature.  Among  the  various  attempts  at 
an  explanation  of  the  series  spectra,  the  theory  of  the  atom  by  Bohr 
deserves  special  attention  because  it  involves  h  and  accounts  with  very 
surprising  accuracy  for  the  Rydberg  constant  of  the  Balmer  and  related 
series.  According  to  Bohr  the  atom  consists  of  a  nucleus  surrounded 
by  electrons  revolving  in  stationary  non-radiating  orbits,  for  which  the 
laws  of  electrostatics  hold  so  that  we  have  : 

ee\      mv2 
~a?  =''  ~a    ' 

The  stationary  circles  are  determined  by  the  postulate  that  the  kinetic 
energy  y<#mP  is  proportional  to  the  quantum  of  energy  such  that 


(z  =  integer) 
mv2irna  =  zhn 


mva 

27T 


hence  the  constant  h  is  proportional  to  the  moment  of  momentum  of  the 
revolving  electron.  It  is  also  proportional  to  the  magnetic  moment 
M  of  the  electron  in  the  stationary  orbit,  thus 

e 
M  =  Tra2i  =  7ra2en  =  zh  -  . 

47TW 

The  non-radiating  orbit  of  the  electron  seems  to  account  at  once  for 
the  constant  magnetic  properties  of  the  elements  and  their  compounds. 


60  JAKOB   KUNZ. 

When  the  electron  moves  from  an  outer  to  an  inner  stationary  orbit,  it 
loses  a  quantum  of  energy,  giving  rise  to  a  line  in  the  spectrum  ; 


27r2me2ei2 


Two  of  the  fundamental  problems  seem  to  be  solved  at  the  same  time, 
the  electron,  when  jumping  from  an  outer  to  an  inner  stationary  orbit 
giving  rise  to  light  and  when  moving  undisturbed  in  a  stationary  orbit, 
producing  the  magnetic  effects.  Of  course  even  if  both  parts  of  the 
theory  were  verified,  the  question  would  still  remain,  why  such  non- 
radiating  orbits  are  possible,  in  other  words,  why  Maxwell's  theory  of 
electromagnetic  radiation  does  not  hold  within  the  atom.  If  this  theory 
is  invalid  within  the  atom,  then  we  might  expect  also  that  the  theory 
of  relativity  does  not  hold  in  the  same  regions. 

Before  I  proceed  to  the  discussion  of  magnetism  on  the  basis  of  Bohr's 
theory,  I  wish  to  call  attention  to  an  interesting  conclusion  with  regard 
to  the  velocities  of  those  electrons  near  the  nucleus  which  give  rise  to 
the  Roentgen  spectra,  the  approximate  law  of  which  has  been  discovered 
by  Moseley.  The  square  root  of  the  highest  frqeuencies  from  the  atoms 
of  the  chemical  elements  is  proportional  to  the  charge  e\  of  the  nucleus. 
This  law  follows  from  Bohr's  theory.  If  we  call  the  nuclear  charges  of 
two  atoms  en  and  e12  and  assume  the  factor  i/z2  —  i/zi2  to  be  the  same 
in  both  elements,  then  we  obtain  from  equation  (i)  for  the  highest  fre- 
quencies of  the  two  elements 

n\ 


where  NI  and  7V2  are  the  corresponding  atomic  numbers.  Now,  Millikan 
has  tested  this  relation  for  tungsten  and  hydrogen  and  has  concluded 
that  the  shortest  wave-length  which  could  be  produced  by  hydrogen  is 
91.4,  while  Lyman  found  for  the  convergence  wave-length  91.2/4/4. 
This  would  correspond  to  the  highest  frequency  of  the  hydrogen  atom. 
It  seems  certain  that  the  Lyman  ultra-violet  series  of  hydrogen  lines 
is  the  K  series  of  this  element.  While  this  agreement  is  very  satisfactory, 
it  should  be  remarked  that  we  have  as  yet  no  proof  of  the  existence  of 
Balmer  series  in  the  Roentgen  spectra,  and  the  resolving  power  of  the 
crystals  for  the  characteristic  Roentgen  rays  may  be  too  small,  so  that 
it  remains  impossible  with  the  present  experimental  means  to  discover 
series  analogous  to  Balmer  series  in  the  Roentgen  spectra.  Now  the 
relation 


1^1  =  eJL 
>  H        6 


62       N2 


VoL.^XII.J  QN   BOHR>s  ATOM   AND   MAGNETISM.  6 1 

may  be  true,  even  if  Bohr's  theory  of  the  atom  is  not  true,  provided  we 
introduce  the  quantum  relation  in  the  following  way,  as  has  been  shown 
by  F.  Sanford.1 

s*  r 

1)  y&wv2  =  hn  v  =  2irna  =  \l —  \n 

\  ^Yt 

mva  =  h/ir 

2)  mv2/a  =  eei/ a2     e\  =  mv2a/e  =  =  vh/ire 

ire 


62.      nz 

Whether  we  deduce  this  relation  according  to  Sanford 's  or  to  Bohr's 
method- we  assume  in  both  cases  that  the  mass  m  of  the  electron  is  the 
same  in  both  and  in  all  elements. 

In  the  theory  of  relativity  the  ratio  of  the  transversal  mass  m  of  the 
moving  electron  to  the  mass  m^  of  the  electron  at  rest  is  given  by 

m  i 


mQ          i  -  v2 


If  we  assume  i.oi  for  w/w0  we  find  v  =  4.2  -io9  cm.  per  sec.  If  the 
shortest  wave-length  X  measured  for  tungsten  is  equal  to  o.i67-io~8 
cm.  then 

n  =^-  =  i.8-io1& 

A 


but 

eei  mv2 
—  =  -  - 
a2  a 


2  i  2i  2  4 

From  (4) 

£l  =  Oj 

ez  ~  ai 
1  PHYSICAL  REVIEW,  Vol.  IX.,  p.  383,  1917. 


62  JAKOB   KUNZ.  [slms. 

for  two  different  elements. 


For  the  hydrogen  atom 

0i  =  5-5-io-9cm. 
for  tungsten 

Ni     Ji 

N2      74' 
hence 

a2  =  743'io~n  cm. 

for  the  innermost  orbit  of  the  electron  in  the  tungsten  atom,  and  the 
circular  velocity 

v2  =  2irna2  =  8.38 -io+9  cm. 

For  the  uranium  atom  we  would  find  a  path  velocity  of  the  electron  in 
the  innermost  orbit  amounting  to  2.I-IO10  cm.,  approaching  somewhat 
the  velocity  of  light.  This  velocity  would  correspond  to  a  mass 
m  =  1.4^0,  if  we  neglect  the  influence  of  other  revolving  electrons. 
It  is  remarkable  that  these  highest  velocities  of  revolving  electrons  remain 
only  about  30  per  cent,  below  the  velocity  of  light,  on  the  other  hand  a 
satisfactory  theory  of  the  Roentgen  spectra  must  take  this  effect  into 
account  or  deny  relativity  in  the  interior  of  the  atom. 

The  velocity  of  the  electrons  in  the  orbits  of  Bohr's  atom  is  so  great, 
that  it  seems  possible  to  explain  the  magnetic  properties  of  the  elements 
by  the  assumption  of  a  few  electrons  revolving  in  nonradiating  orbits. 
We  shall  proceed  to  compare  the  magnetic  properties  of  some  of  the  sim- 
plest elements  with  Bohr's  theory  of  the  atoms  and  molecules.  The 
first  difficulty  which  we  encounter  consists  in  the  fact  that  we  have 
measured  so  far  only  the  magnetic  properties  of  molecules  (except  the 
rare  gases)  and  not  of  atoms  and  that  Bohr's  theory  of  the  molecules, 
of  hydrogen  for  instance,  is  not  so  definite  as  that  of  the  atoms.  The 
hydrogen  atom  consists  of  a  nucleus  of  charge  e\  and  an  electron  of 
charge  e,  revolving  in  a  circular  orbit  around  about  the  nucleus.  This 
atom  represents  an  elementary  magnet  and  if  the  hydrogen  gas  were 
made  up  of  atoms  it  would  be  paramagnetic  and  the  paramagnetic  sus- 
ceptibility could  be  evaluated  at  once.  But  now  the  question  arises 
as  to  the  nature  of  the  coupling  of  two  atoms  in  a  molecule.  The  ele- 
mentary magnets  of  two  atoms  may  arrange  themselves  so  that  the  axes 
of  the  two  magnetons  form  the  same  line,  hydrogen  would  then  still  be 
paramagnetic,  or  the  axes  may  be  parallel  to  each  other  and  the  neigh- 
boring poles  be  of  opposite  sign,  the  hydrogen  gas  would  then  be  dia- 


No^'i*11']  ON   BOHR'S   ATOM   AND    MAGNETISM.  63 

magnetic;  finally,  and  this  is  the  case  Bohr  has  assumed  for  the  hydrogen 
molecule,  both  electrons  revolve  in  the  same  orbit,  separated  by  180°, 
the  plane  of  the  orbit  being  at  right  angles  to  the  line  joining  the  two 
nuclei.  Bohr  calculates  for  the  radius  of  the  common  orbit  of  the 
electrons  a  =  5.22-io~9  cm.,  for  the  frequency  n  =  6.72  -io15.  This  gas 
is  paramagnetic.  The  magnetic  moment  M  is  equal  to  : 

M  =  2-jra2en  =  1.82-iQ-20 
The  magnetic  susceptibility  at  o° 

NM2  _  2.72-io19(i.82)2-io-40 
~3*T  =       3-1,  37"  io16-  273 

k  =  +  8.2  •  io~8  per  unit  volume  at  o°. 

The  values  which  I  find  in  the  literature  are  contradictory:  +  o.8-io~8 
(Quincke),  —  o.5-io~8  (Bernstein),  —  o.34-io~8  (Blondlot).  A  further 
accurate  determination  of  the  magnetic  properties  of  hydrogen  is  very 
necessary. 

The  helium  atom  in  Bohr's  theory  consists  of  a  nucleus  of  charge  2e 
around  which  there  are  rotating  2  electrons  in  the  same  orbit  of  radius 
a  =  o.3i4'io~8  cm.,  with  a  frequency  n  =  19.  io15.  This  gas  would  be 
paramagnetic.  The  magnetic  moment  of  the  atom  is  equal  to  1  .85  •  io~20, 
the  susceptibility  k  =  8.5  -io~8  at  o°;  for  both  gases  k  =  C/T  where 
Curie's  constant  C  =  NM2/^R.  Helium  like  the  other  inert  gases  is 
diamagnetic.  Here  Bohr's  theory  is  in  contradiction  with  the  experi- 
mental fact. 

Lithium  is  supposed  to  contain  a  nucleus  of  charge  30;  two  electrons 
revolve  in  the  inner  orbit  and  one  electron  in  the  outer  orbit  in  the 
same  direction,  giving  rise  to  paramagnetism  ;  the  magnetic  moment 
can  easily  be  calculated. 

M  =  2ira12en1  +  ira22en2  =  2.815-  icr20, 
01  =  i.99-io~9  a2  =  0.651  -icr8, 

HI  =  4.74  -io16  n2  =  443  -io15. 

The  paramagnetic  susceptibility  of  lithium  would  be  equal  to: 


NM2      2.72  •  io19(2.8i5)2io-40 
3  -i.  37  -io-16  273 


.  . 

k  =  ~^  =  -  —  =   +  I.Q8-IQ-7 

-16 


per  unit  volume  at  o°.     Lithium  like  the  other  alkali  metals  is  weakly 
paramagnetic.     The  literature  contains  the  value  2.26-  io~7,  which  agrees 


64  JAKOB    KUNZ.  [!ER?ESD 

with  the  theoretical  value  even  better  than  we  should  expect,  because 
we  have  treated  lithium  like  a  gas,  while  for  the  solid  state  the  mutual 
action  of  the  elementary  magnets  must  be  taken  into  account. 

Finally,  beryllium,  in  Bohr's  theory,  consists  of  a  nuclear  charge  40 
with  two  orbits,  each  containing  two  electrons.  If  the  radii  and  the 
frequencies  of  the  electrons  in  the  neutral  state  of  the  atom  were  uniquely 
determined,  the  magnetic  moment  and  the  magnetic  susceptibility  could 
easily  be  calculated.  The  atom  model  is  paramagnetic  in  agreement 
with  experimental  determinations. 

All  four  substances,  hydrogen,  helium,  lithium,  beryllium,  are  para- 
magnetic according  to  Bohr's  theory,  while  hydrogen  is  probably  dia- 
magnetic  and  helium  is  almost  certainly  diamagnetic.  The  effect  of  a 
magnetic  field  on  a  paramagnetic  gas  consists  in  the  orientation  of  the 
molecular  magnets  into  the  direction  of  the  external  field;  so  that  there 
will  be  a  state  of  equilibrium  between  the  directing  tendency  of  the  field 
and  the  disturbing  tendency  of  the  temperature  agitation.  As  far  as 
this  effect  of  the  field  is  concerned,  we  are  justified  in  applying  the  theory 
of  paramagnetism  to  Bohr's  atom  model.  But  the  field  must  also  have 
a  secondary  effect  on  paramagnetism,  an  effect  which  determines  at  the 
same  time  the  diamagnetic  properties. 

Let  us  consider  in  a  diamagnetic  gas  an  atom  with  an  electronic  orbit 
of  radius  a,  the  electron  e  revolving  with  velocity  v  in  a  plane  perpen- 
dicular to  the  magnetic  field.  The  magnetic  moment,  without  the 
action  of  the  external  field,  will  be  equal  to  M  =  Tra2en-  if  a  field  H  is 
applied  the  frequency  will  change  so  that 

dM  =  7re(2anda  +  a2dn) 
or  assuming  the  first  term  small, 

jnp 

dM  =  irea2dn  =  —  irea2  —  . 

But  in  the  theory  of  diamagnetism  as  well  as  in  Lorentz's  theory  of  the 
simple  Zeeman  effect,  it  is  assumed  that 

mv2- 


that  is,  the  centripetal  force,  which  balances  the  centrifugal  force  is  pro- 
portional to  the  distance  a  between  the  electron  and  the  center  of  the 
atom,  the  centripetal  force  is  a  quasi  elastic  force;  while  in  Bohr's  theory 
the  centripetal  force  is  inversely  proportional  to  the  square  of  the  dis- 
tance between  the  electron  and  the  nucleus.  Yet  even  under  these 
circumstances  we  can  find,  allowing  certain  approximations,  the  older 


No^"iXIL]  ON   BOHR'S  ATOM   AND   MAGNETISM.  65 

expressions  for  the  diamagnetic  susceptibility  and  for  the  Zeeman  effect, 
except  for  a  factor  2,  as  will  be  seen  from  the  following  deductions  which 
are  self  explanatory. 

mv2      f 
a        a? 
With  a  magnetic  field  we  have  : 

mv2       f  mv2a 

—  =  -2  -  Hev  =  -7,-  -  Hev 

mv2      mv2a  Hev 

a'2         a'3  a' 

2ira        2ira' 


—  =  j^  =  ~,  =  Constant, 


He 

2irm  \  -^72  —  i^>  — ;  I    =    —  -=f  , 

He 

2irm  ' 


a/s 


_He 

but 

a'  =  a  +  da,     a'3  =  a3  +  $a2da     Tr  =  T  +  dT,     T'2  =  T2  - 
hence 

He 

-  T,  i 

da  =^dT  =  (2Tra/2wT)dT  =  °^dTt 
He 


"3     *  =  ~  He' 


dr  He 

—  =  —  an  =  --    -  =  HI  —  nt 
jf2  2irm 

He 

=  n  —  HZ, 


He 


66  JAKOB   KUNZ. 

which  is  the  formula  for  the  Zeeman  effect  except  for  the  factor  J^. 
This  explanation  of  the  Zeeman  effect  is  open  to  a  logical  objection; 
namely,  in  Bohr's  theory  it  is  assumed  that  a  line  of  the  spectrum  is 
emitted  when  an  electron  moves,  we  do  not  know  on  which  path,  from 
an  outer  to  an  inner  non-radiating  orbit.  The  magnetic  field,  of  course, 
acts  on  the  electron  during  the  emission  of  light;  that  is,  while  the 
electron  moves  from  one  orbit  to  the  other.  But  in  this  present  theory, 
as  in  the  older  Lorentz  theory,  we  assume  that  the  magnetic  field  affects 
only  the  stationary  orbits. 

This  assumption  however  remains  valid  for  the  determination  of  the 
diamagnetic  susceptibility  which  we  shall  now  consider. 


2 

dM-     -«*'^-  =   --. 

If  there  are  N  orbits  per  unit  volume  and  if  the  axes  are  uniformly 
distributed  in  all  directions,  then  we  have 

eWNH 
M  =        ,-     , 
6M 

or,  the  diamagnetic  susceptibility  k  is  equal  to 


k  = 

6m    ' 

or,  twice  as  large  as  the  same  quantity  calculated  on  Lorentz's  assumption 
that  the  centripetal  forces  are  proportional  to  the  distance  between 
the  electron  and  the  center  of  the  atom.  For  the  diamagnetic  suscepti- 
bility and  for  the  Zeeman  effect  we  have  to  assume  in  Bohr's  atom 
that  under  the  influence  of  the  magnetic  field  the  nonradiating  orbits 
are  slightly  changed. 

For  a  paramagnetic  gas   the  resultant  susceptibility  would   be   the 
difference 

3#r   "       6m    ' 
For  hydrogen  we  would  have 

4.7r2a*eVN      e2a?N2 

k  = 


If  we  take  again  for  oc 


ON   BOHR'S  ATOM   AND   MAGNETISM. 


a  =  5.22  -lo-9, 
n  =  6.72-I015, 
m  =  9.01  -lO"28, 
R  =  I.37-IO-16, 

T  =  273. 
We  find: 


—  =  3-7 -io26, 

that  shows  that  the  paramagnetic  effect  for  hydrogen  at  o°  is  more 
than  i  ,000  times  larger  than  the  diamagnetic  effect. 

For  helium  we  have  the  corrected  paramagnetic  susceptibility  equal  to : 

NaM* 

K    — 


6m 

M  —  2ira?en, 


With  the  previously  given  values  for  the  radius  a  and  the  frequency 
n  of  the  electrons  we  find 

222 

=  I.26-I030. 


The  relative  diamagnetic  effect  of  helium  is  a  little  smaller  than  the 
corresponding  effect  of  hydrogen. 

In  general,  the  observed  susceptibility  k  is  the  difference  between  the 
paramagnetic  susceptibility  kp  and  the  diamagnetic  susceptibility  ka 

k  =  kp  —  kd. 

It  is  therefore  quite  conceivable  that  an  element  like  tin  changes  at 
given  temperatures  from  the  negative  to  the  positive  sign  of  magnetism, 
and  vice  versa;  kp  at  all  events  is  a  function  of  temperature.  For  the 
diamagnetic  gases  the  susceptibility  is  probably  almost  independent  of 
temperature.  If  Bohr's  theory  of  the  structure  of  helium  is  in  the  right 
direction  toward  the  physical  reality  then  we  have  to  make  a  little 
modification  in  order  to  explain  the  magnetic  properties  of  helium.  If 
the  principle  of  conservation  of  the  moment  of  momentum  holds  within 


68  JAKOB    KUNZ. 

\ 

the  atom,  if  this  momentum  is  proportional  to  the  magnet  moment  and 
if  the  electrons  are  moving  in  elliptic  orbits,  then  the  nucleus  would  also 
move  around  the  center  of  attraction  of  the  system,  in  the  same  direction 
as  the  electrons,  the  magnetic  moments  of  the  electrons  and  the  nucleus 
would  balance  each  other  and  the  atom  would  be  diamagnetic.  Of 
course,  it  is  not  required  that  the  resultant  moment  should  be  exactly 
zero,  but  only  that  the  absolute  value  of  kd  should  be  larger  than  kp. 
If  over  a  wide  range  of  temperature  of  a  gas  k  were  independent  of  the 
temperature  then  kp  would  be  equal  to  zero.  The  Zeeman  effect  of  iron 
vapor  shows  that  the  diamagnetic  properties  persist  up  to  very  high 
temperatures,  and  the  additive  law  of  diamagnetism  for  organic  com- 
pounds of  similar  constitution  indicates  that  the  diamagnetism  is  a 
rather  deep  seated  property  of  matter,  which  may  be  attributed  partly 
to  the  nucleus.  On  the  other  hand  the  paramagnetic  phenomena  and 
the  diamagnetic  properties  of  solid  and  liquid  substances  are  readily 
influenced  by  chemical  and  mechanical  agencies. 

SUMMARY. 
i.  It  has  been  shown  that  the  relation 

1 


can  be  deduced  by  means  of  the  quantum  relation  without   Bohr's 
theory  of  the  atom. 

2.  If  we  calculate  the  radii  of  the  orbits  and  the  velocities  v  of  the 
electrons  near  the  nucleus  of  the  atom  by  means  of  the  relations  : 

ei  N! 

a2  =  di  -  =  ai  —  , 

e2  N2 

V2  =  2irna2, 

we  find  for  the  greatest  velocity  of  the  electrons  in  the  uranium  atom 
2.I-IO10  cm.  corresponding  to  a  mass  m  of  the  electron  equal  to  i.4W0. 

3.  The  paramagnetic  moments  and  the  paramagnetic  susceptibilities 
of  hydrogen,  helium  and  lithium  have  been  calculated  by  means  of 
Bohr's  theory.     If  hydrogen  really  is  diamagnetic,  which  has  yet  to 
be  decided  by  experimental  measurements,  the  magnetic  properties  of 
hydrogen  and  helium  can  not  be  explained  by  Bohr's  atom-model.     In 
this  case  a  new  model  has  to  be  invented,  or  the  magnetic  properties 
have  to  be  ascribed  to  different  causes,  for  instance,  to  proper  magnetons, 
independent  of  revolving  electrons,  or  to  electrons  whose  charge  itself  is 


NoL'iXIL]  ON   BOHR'S  ATOM   AND   MAGNETISM.  69 

in  motion,  so  that  the  electron  is  at  the  same  time  a  magneton  or  to  the 
nucleus  as  being  responsible  partly  for  the  magnetic  phenomena. 

4.  A  modification  of  the  simple  Zeeman  effect  has  been  given.     The 
resultant  equation 

He 

#2  —  n\  =  — 

7TW 

differs  from  Lorentz's  theory  by  the  factor  %. 

5.  The  diamagnetic  susceptibility  of  hydrogen  and  helium  has  been 
calculated.     It  is  about   1,000   times  smaller  than   the  paramagnetic 
susceptibility. 

6.  A  modification  of  Bohr's  atom  has  been  considered,  which  will 
account  for  the  diamagnetic  properties  of  He. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
April,  1918. 


THE   MAGNETIC    PROPERTIES  OF  SOME   RARE   EARTH 
OXIDES  AS  A  FUNCTION  OF  THE  TEMPERATURE. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.  S.,  Vol.  XII,  No.  2,  August,  1918.] 


THE  MAGNETIC   PROPERTIES  OF  SOME  RARE  EARTH 
OXIDES  AS  A  FUNCTION  OF  THE  TEMPERATURE. 

BY  E.  H.  WILLIAMS. 

THE  existence  or  non-existence  of  the  magneton,  the  elementary 
quantity  of  magnetism  corresponding  to  the  electron  of  elec- 
tricity, has  attracted  the  attention  of  investigators  since  it  was  first 
suggested  by  Ritz.  Much  work  has  been  done,  especially  by  Weiss, 
Kammerling  Onnes,  du  Bois,  Honda,  Perrier.  Piccard  and  Terry,  and 
while  the  preponderance  of  the  results  obtained  by  these  investigators 
is  against  the  elementary  moment  of  magnetism  as  suggested  by  Weiss, 
yet  the  idea  is  still  strongly  maintained  by  some.  Within  the  last  three 
years  Piccard1  maintains  that  there  is  a  group  of  bodies  (paramagnetic) 
which  obey  strictly  Curie's  law  and  hence  he  argues  that  the  foundations 
of  the  theory  are  sound  and  there  is  still  evidence  in  favor  of  the  magneton. 

Not.  only  was  it  hoped  to  get  evidence  for  or  against  the  magneton 
theory,  but  the  opportunity  to  obtain  from  the  Chemistry  Department 
of  the  University  of  Illinois  rare  earths  in  a  very  pure  state  from  which 
were  being  made  atomic  weight  determinations  made  it  desirable  to 
investigate  their  magnetic  constants.  My  thanks  are  due  to  Dr.  Hopkins 
and  his  associates  of  the  Chemistry  Department  for  their  hearty  co- 
operation in  supplying  me  with  samples  of  the  rare  earth  materials. 

The  method  used  was  that  of  Curie2  which  consists  in  measuring  the 
pull  exerted  on  an  object  placed  in  a  non-uniform  magnetic  field.  Accord- 
ing to  this  method  X,  the  magnetic  susceptibility  per  unit  mass,  is  given 
by  the  expression 


OX 

providing  the  force  is  measured  by  means  of  the  twist  of  a  suspension. 
In  this  expression  M  is  the  mass  of  the  sample,  Hv  the  field  at  right  angles 
to  the  direction  of  motion  of  the  sample,  dHy/dx  the  variation  of  this 
field  along-  the  direction  of  motion,  C  the  couple  necessary  to  twist  the 

1  Piccard,  Arch,  des  Sci.  Phys.  et  Nat.,  40,  278,  1915. 

2  P.  Curie,  Ann.  de  Chem.  et  de  Phys.,  (7),  5,  298,  1895. 


VOL.  XII. 
No.  2. 


MAGNETIC   PROPERTIES   OF   RARE   EARTH   OXIDES. 


suspension  through  one  radian,  <f>  the  angle  of  twist  in  radians  and  /  the 
lever  arm  from  the  line  of  suspension  to  the  sample. 

The  torsion  balance  was  contained  in  a  wooden  box  put  together 
without  the  use  of  any  magnetic  material.  The  suspension  consisted  of 
a  phosphor-bronze  wire  the  torsion  couple  of  which  was  940  dyne  cm.  at 
25°  C.  It  was  found  that  this  varied  with  the  temperature,  the  variation 
being  about  —  0.6  dyne  cm.  for  i°  C.  Since,  in  some  cases,  the  box 
containing  the  torsion  balance  warmed  up  five  or  six  degrees  Centigrade, 
a  correction  was  made  for  the  variation  of  the  torsion  couple. 

During  the  first  part  of  the  work  an  aluminum  rod  was  used  for  the 
lever  arm  and  pointer  of  the  balance  but  the  zero  corrections  for  this 
were  so  large  that  it  was  deemed  advisable  to  find  another  system.  The 
system  finally  adopted  consisted  of  glass  which  was  slightly  diamagnetic 
counterpoised  with  a  small  amount  of  aluminum  which  was  slightly 
paramagnetic.  By  using  the  right  amount  of  aluminum  the  zero  correc- 
tion could  be  made  very  small. 

Several  sets  of  values  of  Hy  and  dHy/dx  were  plotted  and  from  the  mean 
curve  values  were  taken  for  the  product  Hy(dHy/dx).  These  products 
were  in  turn  plotted  and  the  point  in  the  field  where  the  product  was  a 
maximum  was  determined.  The  apparatus  was  now  set  so  that  the  center 
of  the  test  coil  was  at  the  point  in  the  field  where  the  product  Hy(dHy/dx) 
was  a  maximum  and  the  values  of  Hy  and  dHy/dx  determined  for  various 
currents  in  the  electromagnet.  The  mean  of  four  such  sets  is  given  in 
Table  I. 

TABLE 'I. 


/. 

H. 

&HI&X. 

//(A/r/A^r.) 

1.5  amp. 

1020 

205.4 

209.5  X  103 

2.0 

1352 

273.7 

370.1 

2.5 

1687 

338.5 

571.1 

3.0 

2012 

407.2 

819.2 

3.5 

2351 

473.0 

1112.1 

4.0 

2659 

530.7 

1411.0 

4.5 

2968 

596.4 

1770.0 

5.0 

3267 

648.9 

2120.0 

The  couple  C  necessary  to  twist  the  suspension  through  unit  angle  was 
found  by  the  ordinary  vibration  method.  An  accurately  turned  disc 
and  ring  were  used  for  known  moments  of  inertia  and  C  calculated  from 
the  formula 

C--*^-  (2) 

U    ~~    ft'*    __    A\   »  \2  ) 


i6o 


E.    H.    WILLIAMS. 


["SECOND 
[SERIES. 


where  7  is  the  known  moment  of  inertia  added  to  change  the  period  from 
t  to  tf. 

The  oxides  of  seven  of  the  rare  earths,  namely,  erbium  (Er2O3), 
dysprosium  (Dy2O3),  gadolinium  (Gd2O3),  samarium  (Sa2O3),  neodymium 
(Nd2O3),  lanthanum  (La2O3)  and  yttrium  (Yt2O3),  were  investigated. 
Before  using  any  of  the  oxides,  they  were  heated  to  a  temperature  of 
about  1000°  C.  in  a  platinum  crucible  in  order  to  decompose  any  carbonate 
which  may  have  formed  and  to  drive  off  all  moisture. 

The  samples  under  investigation  were  contained  in  a  silica  capsule 
which  was  fitted  to  one  arm  of  the  torsion  balance.  The  balance,  with 
thermocouple  and  empty  capsule  in  place,  was  first  calibrated  for  fields 
due  to  currents  of  from  1.5  to  5  amperes  and  for  temperatures  from  25°  C. 
to  300°  C. 

Table  II.  gives  a  sample  set  of  data  for  Gd2O3  with  the  thermocouple 


"Mass  of  sample  =  .11912  gm. 
torsion  balance  =  105.7  cm. 


TABLE  II. 

99  +  Per  Cent.  Pure. 
Lever  arm  of  sample  =  10.55   cm. 


Scale   distance   of 


Temp. 

Current  in 
Magnet. 

Deflection  of 
Torsion  Balance. 

Corrected  Deflec- 
tion. 

XX*. 

21.8°  C. 

1.5  amp. 
2.0 
2.5 
3.0 

7.81  cm. 
13.79 
21.31 
30.21 

7.59  cm. 
13.47 
20.93 
29.86 

128.3 
128.9 
129.8 
129.1 

. 

Mean  

129.0 

103.2 
11 

1.5 
2.0 
2.5 
3.0 
3.5 

6.12 
11.11 

16.80 
23.74 
31.82 

5.98 
10.93 
16.64 
23.61 
31.75 

101.1 
104.6 
103.2 
102.1 
101.1 

Mean  

102.4 

178.0 

1.5 
2.0 
2.5 
3.0 
3.5 

5.16 
9.13 
14.15 
20.03 
26.63 

5.07 
9.04 
14.10 
20.03 
26.73 

85.5 
86.3 
87.2 
86.4 
84.9 

Mean       

86.1 

269.5 
ii 

1.5 
2.0 
2.5 
3.0 
3.5 

4.15 
7.43 
11.65 
16.49 

21.87 

4.07 
7.37 
11.63 
16.59 
22.10 

68.6 
70.3 
71.9 
71.5 
70.2 

Mean 

70.5 

VOL.  XII." 
No.  2. 


MAGNETIC   PROPERTIES   OF   RARE   EARTH   OXIDES. 


161 


and  torsion  balance  readings  omitted.  Four  such  sets  of  data  were 
taken  with  different  samples  of  the  same  material.  One  curve  repre- 
senting the  four  sets  of  data  was  drawn  in  which  magnetic  susceptibility 
was  plotted  against  temperature.  From  this  curve  values  were  taken 
to  test  Curie's  law. 

In  like  manner  the  other  oxides  were  tested  and  results  plotted. 
From  these  curves  the  results  in  the  first  and  third  columns  of  Tables 
III.,  IV.,  V.  and  VI.  were  obtained.  For  each  temperature  the  value  of 
the  magnetic  susceptibility  X,  is  the  mean  of  the  values  obtained  from 
four  or  five  fields  as  in  Table  II. 


TABLE  III. 

Gadolinium  Oxide  QQ  +  Per  Cent.  Pure. 


t. 

T. 

XX  io6. 

XTX  io«. 

jrcr+i2)xio6. 

20 

293 

130.1 

38119 

39680 

60 

333 

115.1 

38328 

39709 

120 

393 

98.2 

38593 

39771 

180 

453 

85.5 

38731 

39757 

240 

513 

75.6 

38783 

39690 

300 

573 

67.8 

38849 

39663 

TABLE  IV. 

Erbium  Oxide  QQ.6  +  Per  Cent.  Pure. 


t. 

T. 

A'X  io<5. 

XTX  io«. 

*'(  T+  13.5)  X  io«. 

20 

293 

189.1 

55406 

57954 

60 

333 

167.2 

55678 

•  57935 

120 

393 

142.6 

56042 

57967 

180 

453 

124.4 

56354 

58033 

240 

513 

110.1 

56462 

57969 

280 

553 

102.2 

56516 

57895 

TABLE  V. 

Dysprosium  Oxide  09.5  +  Per  Cent.  Pure. 


t. 

T. 

XX  io<5. 

XTX  106. 

A'(  T+  15)  X  106. 

20 

293 

234.1 

68591 

72103 

60 

333 

207.4 

69064 

72175 

120 

393 

176.7 

69443 

72094 

180 

453 

153.9 

69717 

72025 

240 

513 

136.6 

70076 

72125 

300 

573 

122.6 

70250 

72089 

162 


E.    H.    WILLIAMS. 


[SECOND 

[SERIES. 


TABLE  VI. 

Neodymium  Oxide  99.5+  Per  Cent.  Pure. 


t. 

T. 

A'Xioe.x 

A'7'X  io6-     j  X(  T+  44)  X  io6. 

23 

296 

29.3 

8672.8 

9962.0 

103.4 

376.4 

23.7 

8920.7 

9963.5 

179.4 

452.4 

19.8 

8957.5 

9828.7 

283.0 

556 

16.6 

9229.6 

9960.0 

TABLE  VII. 

Samarium  Oxide  99.5+  Per  Cent.  Pure. 

Temp. 

22.3 

101.8 

270.2 


6.02 
5.93 

5.98 


Mean 5.98 

TABLE  VIII. 

Lanthanum  Oxide  99  +  Per  Cent.  Pure. 


Temp. 

Hy. 

Corrected  Def. 

XX  io«. 

24°  C. 

2025 

-0.09 

-0.49 

n 

2660 

-0.13 

-0.41 

« 

3010 

-0.14 

-0.36 

« 

3328 

-0.16 

-0.34 

Mean  

-0.40 

TABLE  IX. 

Yttrium  Oxide  99.5  +  Per  Cent.  Pure. 


Temp. 

Hy. 

Corrected  Def. 

A-X«o». 

22°  C. 

2025 

.09 

.60 

« 

2351 

.11 

.52 

a 

2660 

.13 

.48 

« 

3010 

.17 

.51 

« 

3328 

.21 

.52 

Mean 

.53 

Samarium  oxide,  Table  VII.,  shows  no  variation  of  magnetic  suscepti- 
bility with  temperature.  Three  sets  of  data  similar  to  that  in  Table  II. 
were  taken,  all  of  which  are  summarized  in  Table  VII.  In  the  case  of 
lanthanum  oxide  and  yttrium  oxide,  Tables  VIII.  and  IX.,  the  magnetic 
susceptibility  was  so  small  that  no  attempt  was  made  to  study  the  varia- 
tion of  the  susceptibility  with  the  temperature.  In  the  case  of  lanthanum 
oxide  the  magnetic  susceptibility  is  negative,  thus  indicating  that  this 
oxide  is  diamagnetic  whereas  all  the  others  are  paramagnetic. 


NoL'2XIL]          MAGNETIC   PROPERTIES   OF   RARE   EARTH   OXIDES.  163 

According  to  Curie's  law  the  susceptibility  of  paramagnetic  bodies 
times  the  absolute  temperature  is  equal  to  a  constant;  that  is,  XT  =  con- 
stant. An  examination  of  Tables  III.,  IV.,  V.  and  VI.  shows  that  the 
law  does  not  hold  for  any  of  the  materials  investigated.  However,  they 
are  found  to  follow  quite  closely  a  modification  of  Curie's  law,  namely, 
the  susceptibility  times  the  absolute  temperature  plus  a  constant  is 
equal  to  a  constant,  X(T  +  0)  =  constant,  in  which  each  material  has 
its  own  value  of  6. 

TABLE  X. 

Williams.  Levy. 

Oxideof  XXIQ6  X  X  io« 

Yttrium  .......................  53  (22°  C.)  -.14 

Lanthanum  ...................      -.40  (24°  C.)  -.18 

Neodymium  ..................     29.3    (23°  C.)  33.5 

Samarium  ....................       5.98  6.5 

Gadolinium  ...................    130.1     (20°  C.)  161. 

Dysprosium  ...................  234.1    (20°  C.)  290. 

Erbium  .......................    189.1     (20°  C.) 

Table  X.  gives  a  summary  of  the  results  obtained  together  with  results 
quoted  by  Levy  in  his  book  on  "The  Rare  Earths,"  page  153,  1915. 

Various  explanations  have  been  advanced  for  the  variation  from 
Curie's  law.  Oosterhuis,1  from  a  consideration  of  zero  point  energy, 
deduces  an  explanation  as  follows: 

Taking  the  value  of  the  rotational  energy  of  the  molecule  as  deduced 
by  Einstein  and  Stern2  to  be 

U  =  ehnikT  _  ~ 

where  h  is  Planck's  constant  and  n  the  frequency  of  the  rotation,  and 
further  assuming  that  this  rotational  energy  is  inversely  proportional 
to  the  magnetic  susceptibility  X  as  developed  by  Langevin,3,  Oosterhuis 
deduces  the  relation 


X(T  +  6)  =  C,     where     6  =  \  •  ^~  . 

6       R 


Since 


47T2/' 


where  /  is  the  moment  of  inertia  of  the  molecule,  he  concludes  that  mole- 
cules with  a  small  moment  of  inertia  will  have  a  large  value  of  6,  a  large 
zero  point  energy  (J/2/m0)  and  deviate  markedly  from  Curie's  law. 

1  Phys.  Zeit.,  14,  862,  1913. 

2  Ann.  d.  Phys.,  40,  551,  1913. 

3  Ann.  Chem.  Phys.,  (8),  5,  70,  1905. 


164 


E.    H.    WILLIAMS. 


[SECOND 

[SERIES. 


Although  the  results  given  above  (Tables  III.,  IV.,  V.  and  VI.)  follow 
a  modified  form  of  Curie's  law,  6  does  not  vary  inversely  as  the  moment 
of  inertia  of  the  molecule  as  is  shown  in  Table  XI. 

TABLE  XI. 


Oxide. 

At.  Wt. 

t. 

Molecular  Wt. 

Molecular  Wt.  X0. 

Erbium  

167.7 

13.5 

383.4 

5176 

Dysprosium  

162.5 

15. 

373.0 

5595 

Gadolinium  
Neodymium  

157.3 
144.3 

12.   . 
44. 

362.6 
336.6 

4351 
14810 

Starting  from  an  entirely  different  viewpoint  Kunz1  has  derived  the 
same  expression  for  the  variation  of  the  magnetic  susceptibility  with  the 
temperature.  He  points  out  that  since  it  is  quite  likely  that  the  electrons 
responsible  for  the  paramagnetism  revolve  in  the  outer  layer  of  the  atom, 
the  molecular  moment  will  be  the  resultant  of  all  the  atomic  moments  of 
the  atoms.  Furthermore,  with  increasing  temperature,  it  is  quite  likely 
that  the  atoms  share  the  energy  of  temperature  agitation  which  also  will 
affect  the  resultant  magnetic  moment  of  the  molecule.  Therefore,  in 
general,  we  may  express  the  molecular  moment  as 

M  =  Mof(T). 

In  solid  or  liquid  paramagnetic  substances  the  forces  which  oppose 
the  tendency  of  the  external  field  to  direct  the  elementary  magnets  is 
composed  of  the  temperature  agitation  R T  together  with  a  force  due  to 
the  mutual  effect  of  the  molecules  on  each  other  and  which  would  be  a 
certain  function  of  the  temperature  fi(T).  With  these  assumptions 
Kunz  obtains  for  particular  values  of  f(T)  and/i(71), 

X(T  +  0)  =  constant. 

All  of  the  substances  included  in  this  investigation  which  vary  with  the 
temperature  obey  the  modified  Curie  law  instead  of  the  law  itself.  In  the 
case  of  samarium  oxide  the  magnetic  susceptibility  is  found  to  be  inde- 
pendent of  the  temperature.  This  is  also  probably  true  of  lanthanum 
oxide  and  yttrium  oxide. 

It  may  appear  from  Table  II.  that  the  magnetic  susceptibility  varies 
with  the  field  strength  thus  indicating  that  the  substance  is  ferromagnetic 
in  nature  but  the  remainder  of  the  data  does  not  bear  out  this  conclusion. 
In  some  cases  the  magnetic  susceptibility  came  out  very  nearly  constant 
for  the  different  field  strengths,  while  in  others  it  varied  in  the  opposite 
way  to  which  it  appears  to  vary  in  Table  II.  A  careful  study  of  all  the 
data  leads  one  to  conclude  that  all  the  oxides  are  paramagnetic. 

1  PHYS.  REV.,  VI.,  2,  113,  1915. 


NoL'2XILl         MAGNETIC   PROPERTIES   OF   RARE   EARTH   OXIDES.  165 

It  was  thought  worth  while  to  test  the  accuracy  of  an  analysis  of  rare 
earths  by  the  magnetic  method.  To  do  this  two  pure  substances  were 
mixed  in  known  proportions  and  the  magnetic  susceptibility  of  the 
mixture  determined.  The  results,  given  in  Tables  XII.  and  XIII. , 
show  very  close  agreement  between  the  percentage  by  weight  and  the 
percentage  by  the  measurement  of  the  magnetic  susceptibility.  The 
magnetic  method  would  not  be  adaptable  if  the  mixture  consisted  of 
more  than  two  substances. 

TABLE  XII. 

Er2O3 09095  gm. 

Yt2O3 .06735  gnu 

Total 15830  gm. 

Per  cent,  of  Er2O3  by  weight 57.45  per  cent. 

Per  Cent,  by  the  Magnetic  Method. 
Substance.  A'X  io«. 

Er2O3  (99.6  per  cent,  pure) 187.7  (at  22.3°  C.) 

Yt2O3  (99.6  per  cent,  pure) ' 53 

Mixture 108.1  (at  22.3°  C.) 

Per  cent.  Er2O3  by  the  magnetic  method 57.71  per  cent. 

TABLE  XIII. 

Per  Cent,  by  Weight. 

Er2O3 06985  gm. 

Sa2O3 .06767  gnu 

Total 13752  gm. 

Per  cent,  of  Er2  O3  by  weight 50.79  per  cent. 

Per  Cent,  by  the  Magnetic  Method. 
Substance.  A'X  106. 

Er2O3  (99.6  per  cent,  pure) 187.9  (at  21.7°  C.) 

Sa2O3  (99.5  per  cent,  pure) 5.98 

Mixture 98.9  (at  21.7°  C.) 

Per  cent,  of  Er2O0  by  magnetic  method 51.08  per  cent. 

SUMMARY. 

The  mass  susceptibilities  for  the  oxides  of  erbium,  dysprosium,  gado- 
linium, samarium,  neodymium,  lanthanum  and  yttrium  have  been  meas- 
ured for  temperatures  from  25°  C.  to  300°  C.  and  all  found  to  be  para- 
magnetic with  the  exception  of  lanthanum  which  was  slightly  dia- 
magnetic. 

In  those  cases  where  the  susceptibility  varies  with  the  temperature 
Curie's  law  is  not  found  to  hold  but  the  results  follow  quite  closely  a 
modification  of  this  law,  namely,  X(T  +  6)  =  constant.  It  follows  that 


1 66  E.   H.    WILLIAMS.  [s£££ 

in  so  far  as  Curie's  law  is  essential  to  the  existence  or  determination 
of  the  magneton  the  results  obtained  are  unfavorable. 

The  magnetic  susceptibility  does  not  vaYy  with  the  field  strength. 

The  results  are  explainable  either  by  the  theory  worked  out  by  Kunz 
or  the  zero  point  energy  theory  of  Oosterhuis. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
URBANA,  ILLINOIS, 
February,  1918. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Voi   XIII.  No.  2,  February,  1919. 


— m-  "awn 

vwwwv «/wvwv\ 


il \MM/W 


WV\ 


Fig.  1. 


AMPLIFICATION   OF  THE   PHOTOELECTRIC   CURRENT   BY 
MEAN3   OF  THE  AUDION. 

BY  CARL  ELI  PIKE. 

A  METHOD  has  been  outlined  by  Jakob  Kunz1  by  means  of  which 
the  photoelectric  current  may  be  amplified,  thus  making  the  photo- 
electric cell  more  useful  as  a  photometer,  especially  in  the  region  of  ultra- 
violet light  and  also  for  technical  purposes. 

The  amplification  is  produced  by 
means  of  a  vacuum  tube  with  three 
electrodes,  or  the  audion.  In  order 
to  determine  the  best  potentials  to 
use  in  the  primary  and  secondary 
circuits  it  is  necessary  to  know  the 
characteristic  curves  for  the  audions 
used.  The  characteristic  curves  of 
several  audions  have  been  deter- 
mined by  an  arrangement  of  apparatus 

shown  in  Fig.  I,  which  is  self  explanatory.  If  we  plot  the  grid  potentials 
as  abscissae  and  the  plate  current  as  ordinates,  the  curve  obtained  is 
called  the  characteristic. 

Due  to  the  fact  that  the  plate  current  as  well  as  the  grid  current  was 
so  sensitive  to  small  changes  in  the  temperature  of  the  filament,  it  was 
necessary  to  keep  the  heat- 
ing current  very  constant. 
Large  storage  cells,  well  insu- 
lated from  the  ground,  were 
used  for  this  purpose.  A 
large  resistance  was  placed 
in  the  external  circuit,  so 
that  a  small  variation  in  the 
resistance  of  the  filament 
would  not  affect  the  current 

appreciably.  The  characteristic  curves  of  three  types  of  audions  are  shown 
in  Figs.  3,  4  and  5.     Audion  no.  I  is  an  oscillion  made  by  the  DeForest 
Radio  Telephone  and  Telegraph  Co.     Audion  no.  2  of  Fig.  4  is  a  W-type; 
1  PHYS.  REV.,  Vol.  X.,  No.  2,  p.  205. 


io3 


CARL  ELI   PIKE. 


[SECOND 

[SERIES. 


Audion  no.  3  of  Fig.  5  is  a  V-type  instrument  made  by  the  Western 
Electric  Co.  It  is  noted  that  the  plate  current  in  the  oscillion  reaches 
its  saturation  value  more  abruptly  than  it  does  in  either  of  the  other  two 
instruments.  In  the  oscillion  it  is  necessary  to  heat  the  filament  to 
incandescence  before  the  electrons  are  emitted,  while  in  audion  W  and 
V  the  light  from  the  filament  was  scarcely  visible. 


Fig.  3. 

Audion  no.  2,  the  W-type  instrument,  was  used  for  the  amplification 
of  the  photoelectric  current,  with  an  arrangement  of  apparatus  shown 
in  Fig.  2.  Twenty- four  volts  were  used  in  the  secondary  circuit  and  a 
hundred  and  twenty-five  volts  in  the  primary.  The  photoelectric  cell 
used  was  a  larger  type  of  those  made  by  Kunz  in  our  laboratory.  With 
125  volts  in  the  primary  circuit,  the  drop  of  potential  inside  the  audion  was 
very  small;  measured  with  an  electrometer  it  was  found  to  be  0.56  volt 
for  nearly  the  highest  intensity  of  light  incident  on  the  photoelectric 
cell.  Since  the  drop  of  potential  between  the  grid  and  filament  is  very 
small  in  comparison  to  that  across  the  terminals  of  the  photoelectric 
cell,  the  photoelectric  current  is  very  nearly  equal  to  what  it  would  be 
if  the  audion  were  out  of  the  circuit.  The  curve  giving  the  relation  be- 
tween the  intensity  of  light  and  the  photoelectric  current  is  shown  in 
Fig.  6.  It  is  unfortunately  not  a  straight  line.  If  this  were  a  straight 
line  and  if  the  portion  of  the  characteristic  curve  of  the  audion,  used  for 
the  amplification,  were  straight,  then  we  would  expect  a  straight  line 
relation  between  the  intensity  of  light  and  the  amplified  current,  and 
the  amplification  iz/ii,  the  ratio  of  the  secondary  to  the  primary  current 
would  be  constant,  represented  by  a  straight  line  parallel  to  the  hori- 


AMPLIFICATION   OF  PHOTOELECTRIC   CURRENT. 


104 


-3  -f 


Fig.  4. 


Fig.  5. 


CARL  ELI  PIKE. 


[SECOND 

[SERIES. 


zontal  axis  of  Fig.  7.  Instead  of  this  straight  line,  the  curve  of  Fig.  7 
has  been  obtained  for  intensities  varying  from  3  to  30  candle  meters. 
For  the  highest  intensity  the  amplification  is  about  1750,  for  the  smallest 


Fig.  6. 

intensity  it  is  over  5,000;  above  an  amplification  of  4,000  the  points  ap- 
pear somewhat  scattered  around  the  curve,  but  this  was  only  so  because 
the  primary  current  deflections  of  the  Leeds  and  Northrup  galvanometer, 


Fig.  7. 

G\  (with  a  figure  of  merit  3.74-io~9  for  the  scale  distance  used),  were 
very  small.  If  the  primary  or  photoelectric  current  i  is  zero,  there  is 
already  a  large  current  through  the  secondary  galvanometer  with  a 


AMPLIFICATION   OF   PHOTOELECTRIC   CURRENT.  IO6 

figure  of  merit  2.g-io~6.  It  goes  without  saying  that  this  "dark"  cur- 
rent was  subtracted  from  that  current  which  was  obtained  in  the  galvan- 
ometer, Gz,  when  the  photoelectric  cell  was  under  the  action  of  light. 
The  difference  between  the  two  deflections  was  proportional  to  the  cur- 
rent iz.  The  deflections  of  the  galvanometers  were  very  steady  and  could 
easily  be  repeated.  Table  I.  gives  the  data  that  have  been  plotted  in 
Fig.  7.  A  satisfactory  theory  of  the  audion,  based  upon  the  motion, 
accumulation  and  absorption  of  electrons  has  not  yet  been  given.  The 
current  amplification  can  therefore  not  yet  be  determined  theoretically. 
But  we  can  find  a  simple  expression  for  the  amplification,  namely, 
iz/ii  in  the  following  way,  which  involves  only  Ohm's  law  and  the  experi- 
mental relation  between  the  plate  current  and  the  grid  potential  ;  as  long 
as  we  restrict  the  amplification  to  the  straight  portion  of  the  character- 
istic iz  =  Cpi,  we  get  the  following  equations. 


RQ  +  RI 


The  amplification  is  therefore  constant  if  C  and  'Ri  are  constants,  that  is, 
if  the  straight  part  of  the  characteristic  is  used  and  if  the  resistance  R!  be- 

^__^       tween   the   filament  and  the 

r~  T~a    ~L  grid  is  constant.     For  large 

"I-H-M  !N-l-H-H-M-H-M-l[  jy,     (£))rt   |j    amplifications  C  and  RI  have 

to  be  large. 

A    different    principle    has 
recently  been  indicated  by  A. 
W.    Hull,1    of    the    General 
Electric    Company,    for    the 
Fig.  8.  amplification    of    small    cur- 

rents.    By   a    proper   choice 

of  the  potentials,  the  electrons  emitted  from  the  incandescent  filament 
pass  through  the  grid  and  strike  the  plate  where  they  are  reflected. 
A  system  of  this  kind,  shown  in  Fig.  8,  presents  a  negative  resistance 
r  between  the  points  a  and  b.  If  we  place  a  photo-electric  cell  with  the 
positive  resistance  R0  in  parallel  with  f,  then  we  get; 

i  P.  I.  R.  E.,  February,  1918. 


CARL   ELI   PIKE. 

TABLE  I. 


[SECOND 

[SERIES. 


Increase  in  <f«. 

ii  Amperes. 

cti. 

/i  Amperes. 

Amplification. 

Intensity  in 
Candle  Meters. 

73.5 

213.0  X  IO-6 

35.0 

131.0  X  IO-9 

1600 

33.0 

64.8 

188.0 

23.5 

87.7 

2100 

24.0 

56.5 

164.0 

17.0 

63.5 

2600 

18.5 

49.0 

142.0 

12.9 

48.2 

2900 

14.8 

41.0 

119.0 

10.0 

37.4 

3270 

12.0 

35.5 

101.5 

8.1 

30.2 

3400 

9.9 

31.4 

91.0 

6.8 

25.4 

3570 

8.3 

28.0 

81.2 

5.7 

21.3 

3800 

7.1 

23.8 

69.0 

4.8 

17.9 

3840 

6.1 

22.5 

65.2 

4.1 

15.3 

4250 

5.3 

19.5 

56.6 

3.5 

13.1 

4320 

4.7 

17.5 

50.7 

3.1 

11.6 

4370 

4.2 

16.5 

47.8 

2.8 

10.5 

4570 

3.7 

15.1 

43.7 

2.5 

9.4 

4680 

3.3 

13.0 

37.7 

2.1 

7.9 

4800 

3.0 

12.0 

34.8 

1.9 

7.1 

4890 

2.7 

10.9 

31.6 

1.8 

6.7 

4720 

2.5 

11.5 

33.3 

1.7 

6.4 

5100 

2.3 

10.0 

29.0 

1.6 

6.0 

4840 

2.1 

10.0 

29.0 

1.5 

5.6 

5200 

1.9 

"W"  type  audion,  no.  2.  Lamp  current,  3.75  amperes;  candle  power,  3.0.  Heating 
current,  0.665  amperes.  B1  equaled  125  volts.  B2  equaled  25  volts.  Figure  of  merit  of  G1 
3.74  X  io~9.  Figure  of  merit  of  G2  2.9  X  io~6  when  shunted  with  1.7  ohm  resistance. 
Ratio  of  figure  of  merit  of  G2  to  that  of  G1  equaled  775. 


and 


hence  the  amplification 


E 


+  r 


may  be  made  very  large  by  making  r  and  R0  nearly  equal  in  absolute 
values. 

One  application  of  the  amplification  of  photoelectric  currents  in  wire- 
less telegraphy  may  be  pointed  out.  J.  Kunz  and  J.  Kemp1  have  at 
first  used  the  photoelectric  cell  as  receiver  in  wireless  telegraphy.  Their 
method  has  been  modified  by  H.  Behnken2  who  showed  that  the 
photoelectric  cell  with  a  string  electrometer  forms  a  constant  detector  of 
high  sensitiveness,  especially  useful  for  photographic  registrations.  With 

1  Jahrbuch  d.  drahtlosen  Telegraphic,  6,  405,  1913. 

2  Verhdlg  d.  deutschen  phys.  Ges.,  16,  p.  668,  1914. 


AMPLIFICATION   OF   PHOTOELECTRIC   CURRENT.  108 

the  amplification  of  the  weak  currents  here  involved  it  should  be  possible 
to  increase  the  usefulness  of  the  photoelectric  detector.  It  was  intended 
to  continue  this  investigation  with  ultra-violet  and  interrupted  light, 
with  alternating  currents,  and  with  a  differential  galvanometer  in  the 
secondary  circuit. 

SUMMARY. 

It  has  been  shown  that  photoelectric  currents  can  be  amplified  by 
means  of  the  audion  from  1,600  to  5,000  times.  The  weaker  the  light 
the  smaller  the  primary  photoelectric  current  and  the  larger  the  ampli- 
fication. With  different  audions  amplifications  of  18,000  have  been 
obtained. 

In  conclusion  the  writer  wishes  to  express  his  appreciation  to  Jakob 
Kunz  for  suggesting  the  problem  and  directing  the  work. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
October,  1918. 


